Publications

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AuthorTitleYearJournal/ProceedingsDOI/URL
An, X., Williams, D.R., Eldredge, J.D. and Colonius, T. Lift Coefficient Estimation for a Rapidly Pitching Airfoil 2020 arXiv:2005.01870  URL 
Abstract: A method for the lift coefficient estimation over a rapidly pitching NACA0009 wing is proposed that contains three components. First, we establish that the Goman-Khrabrov model is in fact, a linear parameter-varying (LPV) system, therefore it is suitable for a Kalman filter without any linearization. In the second part we attempt to estimate the lift coefficient by measuring the surface pressure from four pressure sensors located on the suction side of the wing. We demonstrate that four pressure sensors alone, are not sufficient to capture the lift coefficient variation during the rapidly pitching maneuvers, and this results in non-Gaussian error. In the last part we demonstrate the non-Gaussian error from the pressure estimated lift coefficient introduces additional errors into the estimator when we employ the conventional Kalman filter design. To address this issue, we propose a new method of coupling the model and the measurement through the Kalman filter. It is shown that the proposed Kalman filter is capable of estimating the lift coefficient accurately on a NACA 0009 wing that is undergoing rapidly pitching maneuvers.
BibTeX:
@misc{AnWilliamsEldredgeEtAl2020,
  author = {An, X. and Williams, D. R. and Eldredge, J. D. and Colonius, T.},
  title = {Lift Coefficient Estimation for a Rapidly Pitching Airfoil},
  year = {2020},
  url = {https://arxiv.org/abs/2005.01870}
}
Brouzet, D., Haghiri, A., Talei, M., Brear, M.J., Schmidt, O.T., Rigas, G. and Colonius, T. Role of Coherent Structures in Turbulent Premixed Flame Acoustics 2020 AIAA Journal
Vol. 58(6), pp. 2635-2642 
DOI URL 
Abstract: Spectral proper orthogonal decomposition (SPOD) is applied to direct numerical simulation datasets of a lean and a stoichiometric methane-air turbulent premixed jet flame. SPOD is used to extract the coherent structures that correlate with the radiated sound by using an inner product based on a linearized disturbance energy. Two types of structures are prominent in the data. The first type arises in the jet's shear layer and is linked to the Kelvin-Helmholtz instability, which is an important mechanism of sound generation in nonreacting jets. These structures produce sound through deformation of the flame front in the shear layer. They contain most of the acoustic energy and are dominant at Strouhal numbers (defined based on the jet's diameter and the inlet mean velocity) less than unity. The second type of structures is found near the jet centerline, where large fluctuations of the flame surface are observed. The structures are linked to small nonlinear flame dynamics and to the Orr mechanism. They travel at a speed close to the inlet mean velocity and are important at higher Strouhal numbers. Regardless of their energy content, both types of structures have important contributions to the broadband nature of combustion noise.
BibTeX:
@article{BrouzetHaghiriTaleiEtAl2020,
  author = {D. Brouzet and A. Haghiri and M Talei and M. J. Brear and O. T. Schmidt and G. Rigas and T. Colonius},
  title = {Role of Coherent Structures in Turbulent Premixed Flame Acoustics},
  journal = {AIAA Journal},
  year = {2020},
  volume = {58},
  number = {6},
  pages = {2635--2642},
  url = {https://colonius.caltech.edu/pdfs/BrouzetHaghiriTaleiEtAl2020.pdf},
  doi = {https://doi.org/10.2514/1.j058480}
}
Bryngelson, S.H., Charalampopoulos, A., Sapsis, T.P. and Colonius, T. A Gaussian moment method and its augmentation via LSTM recurrent neural networks for the statistics of cavitating bubble populations 2020 International Journal of Multiphase Flow
Vol. 127, pp. 103262 
DOI URL 
Abstract: Phase-averaged dilute bubbly flow models require high-order statistical moments of the bubble population. The method of classes, which directly evolve bins of bubbles in the probability space, are accurate but computationally expensive. Moment-based methods based upon a Gaussian closure present an opportunity to accelerate this approach, particularly when the bubble size distributions are broad (poly-disperse). For linear bubble dynamics a Gaussian closure is exact, but for bubbles undergoing large and nonlinear oscillations, it results in a large error from misrepresented higher-order moments. Long short-term memory recurrent neural networks, trained on Monte Carlo truth data, are proposed to improve these model predictions. The networks are used to correct the low-order moment evolution equations and improve prediction of higher-order moments based upon the low-order ones. Results show that the networks can reduce model errors to less than 1% of their unaugmented values. (C) 2020 Elsevier Ltd. All rights reserved.
BibTeX:
@article{BryngelsonCharalampopoulosSapsisEtAl2020,
  author = {Spencer H. Bryngelson and Alexis Charalampopoulos and Themistoklis P. Sapsis and Tim Colonius},
  title = {A Gaussian moment method and its augmentation via LSTM recurrent neural networks for the statistics of cavitating bubble populations},
  journal = {International Journal of Multiphase Flow},
  year = {2020},
  volume = {127},
  pages = {103262},
  url = {https://arxiv.org/abs/1912.04450},
  doi = {https://doi.org/10.1016/j.ijmultiphaseflow.2020.103262}
}
Bryngelson, S.H., Charalampopoulos, A., Sapsis, T.P. and Colonius, T. Averaging methods for cavitating bubbly flows 2020 Proceedings of the 33rd Symposium on Naval Hydrodynamics, Osaka, Japan  URL 
Abstract: Averaged models are used to represent cavitating bubbly mixtures at the sub-grid computational level. Though such averaging techniques are widely used, the relative computational performance of various adaptations remains unknown. The accuracy and computational efficiency of two such models, one ensemble-averaging and one volume-averaging, addresses this issue. Results show that the relative computational cost of the methods depends upon the degree of bubble polydispersity. The ensemble-averaged model requires more quadrature nodes for broader population sizes and increasingly broad populations become computationally untenable. A moment-based method addresses this shortcoming. It uses a Gaussian closure and is augmented via long short-term memory recurrent neural networks for high-order statistics. Results show that this approach achieves small relative errors for even high-order statistical moments using only five degrees of freedom, significantly fewer than the hundreds required by classes methods.
BibTeX:
@inproceedings{BryngelsonCharalampopoulosSapsisEtAl2020,
  author = {S. H. Bryngelson and A. Charalampopoulos and T. P. Sapsis and T. Colonius},
  title = {Averaging methods for cavitating bubbly flows},
  booktitle = {Proceedings of the 33rd Symposium on Naval Hydrodynamics, Osaka, Japan},
  year = {2020},
  url = {http://colonius.caltech.edu/pdfs/BryngelsonCharalampopoulosSapsisEtAl2020.pdf}
}
Bryngelson, S.H. and Colonius, T. Simulation of humpback whale bubble-net feeding models 2020 The Journal of the Acoustical Society of America
Vol. 147(2), pp. 1126-1135 
DOI URL 
Abstract: Humpback whales can generate intricate bubbly regions, called bubble nets, via blowholes. Humpback whales appear to exploit these bubble nets for feeding via loud vocalizations. A fully-coupled phase-averaging approach is used to model the flow, bubble dynamics, and corresponding acoustics. A previously hypothesized waveguiding mechanism is assessed for varying acoustic frequencies and net void fractions. Reflections within the bubbly region result in observable waveguiding for only a small range of flow parameters. A configuration of multiple whales surrounding and vocalizing towards an annular bubble net is also analyzed. For a range of flow parameters, the bubble net keeps its core region substantially quieter than the exterior. This approach appears more viable, though it relies upon the cooperation of multiple whales. A spiral bubble net configuration that circumvents this requirement is also investigated. The acoustic wave behaviors in the spiral interior vary qualitatively with the vocalization frequency and net void fraction. The competing effects of vocalization guiding and acoustic attenuation are quantified. Low void fraction cases allow low-frequency waves to partially escape the spiral region, with the remaining vocalizations still exciting the net interior. Higher void fraction nets appear preferable, guiding even low-frequency vocalizations while still maintaining a quiet net interior.
BibTeX:
@article{BryngelsonColonius2020,
  author = {Bryngelson, Spencer H and Colonius, Tim},
  title = {Simulation of humpback whale bubble-net feeding models},
  journal = {The Journal of the Acoustical Society of America},
  year = {2020},
  volume = {147},
  number = {2},
  pages = {1126--1135},
  url = {https://arxiv.org/abs/1909.11768},
  doi = {https://doi.org/10.1121/10.0000746}
}
Bryngelson, S.H., Colonius, T. and Fox, R.O. QBMMlib: A library of quadrature-based moment methods 2020 arXiv:2008.05063  URL 
Abstract: QBMMlib is an open source Mathematica package of quadrature-based moment methods and their algorithms. Such methods are commonly used to solve fully-coupled disperse flow and combustion problems, though formulating and closing the corresponding governing equations can be complex. QBMMlib aims to make analyzing these techniques simple and more accessible. Its routines use symbolic manipulation to formulate the moment transport equations for a population balance equation and a prescribed dynamical system. However, the resulting moment transport equations are unclosed. QBMMlib trades the moments for a set of quadrature points and weights via an inversion algorithm, of which several are available. Quadratures then closes the moment transport equations. Embedded code snippets show how to use QBMMlib, with the algorithm initialization and solution spanning just 13 total lines of code. Examples are shown and analyzed for linear harmonic oscillator and bubble dynamics problems.
BibTeX:
@misc{BryngelsonColoniusFox2020,
  author = {Spencer H. Bryngelson and Tim Colonius and Rodney O. Fox},
  title = {QBMMlib: A library of quadrature-based moment methods},
  year = {2020},
  url = {https://arxiv.org/abs/2008.05063}
}
Dorschner, B., Biasiori-Poulanges, L., Schmidmayer, K., El-Rabii, H. and Colonius, T. On the formation and recurrent shedding of ligaments in droplet aerobreakup 2020 Journal of Fluid Mechanics
Vol. 904, pp. A20 
DOI URL 
Abstract: The breakup of water droplets when exposed to high-speed gas flows is investigated using both high-magnification shadowgraphy experiments as well as fully three-dimensional numerical simulations, which account for viscous as well as capillary effects. After thorough validation of then simulations with respect to the experiments, we elucidate the ligament formation process and the effect of surface tension. By Fourier decomposition of the flow field, we observe the development of specific azimuthal modes, which destabilize the liquid sheet surrounding the droplet. Eventually, the liquid sheet is ruptured, which leads to the formation of ligaments. We further observe the ligament formation and shedding to be a recurrent process. While the first ligament shedding weakly depends on the Weber number, subsequent shedding processes seem to be driven primarily by inertia and the vortex shedding in the wake of the deformed droplet.
BibTeX:
@article{DorschnerBiasiori-PoulangesSchmidmayerEtAl2020,
  author = {Dorschner, Benedikt and Biasiori-Poulanges, Luc and Schmidmayer, Kevin and El-Rabii, Hazem and Colonius, Tim},
  title = {On the formation and recurrent shedding of ligaments in droplet aerobreakup},
  journal = {Journal of Fluid Mechanics},
  year = {2020},
  volume = {904},
  pages = {A20},
  url = {https://arxiv.org/abs/2003.00048},
  doi = {https://doi.org/10.1017/jfm.2020.699}
}
Dorschner, B., Yu, K., Mengaldo, G. and Colonius, T. A fast multi-resolution lattice Green's function method for elliptic difference equations 2020 Journal of Computational Physics
Vol. 407, pp. 109270 
DOI URL 
Abstract: We propose a mesh refinement technique for solving elliptic difference equations on unbounded domains based on the fast lattice Green's function (FLGF) method. The FLGF method exploits the regularity of the Cartesian mesh and uses the fast multipole method in conjunction with fast Fourier transforms to yield linear complexity and decrease timeto-solution. We extend this method to a multi-resolution scheme and allow for locally refined Cartesian blocks embedded in the computational domain. Appropriately chosen interpolation and regularization operators retain consistency between the discrete Laplace operator and its inverse on the unbounded domain. Second-order accuracy and linear complexity are maintained, while significantly reducing the number of degrees of freedom and hence the computational cost.
BibTeX:
@article{DorschnerYuMengaldoEtAl2020,
  author = {Benedikt Dorschner and Ke Yu and Gianmarco Mengaldo and Tim Colonius},
  title = {A fast multi-resolution lattice Green's function method for elliptic difference equations},
  journal = {Journal of Computational Physics},
  year = {2020},
  volume = {407},
  pages = {109270},
  url = {https://arxiv.org/abs/1911.10228},
  doi = {https://doi.org/10.1016/j.jcp.2020.109270}
}
Huertas-Cerdeira, C., Goza, A., Sader, J.E., Colonius, T. and Gharib, M. Dynamics of an inverted cantilever plate at moderate angle of attack 2020 arXiv:2005.07374  URL 
Abstract: The dynamics of a cantilever plate clamped at its trailing edge and placed at a moderate angle (α≤30∘) to a uniform flow are investigated experimentally and numerically, and a large experimental data set is provided. The dynamics are shown to differ significantly from the zero-angle-of-attack case, commonly called the inverted-flag configuration. Four distinct dynamical regimes arise at finite angles: a small oscillation around a small-deflection equilibrium (deformed regime), a small-amplitude flapping motion, a large-amplitude flapping motion and a small oscillation around a large-deflection equilibrium (deflected regime). The small-amplitude flapping motion appears gradually as the flow speed is increased and is consistent with a limit-cycle oscillation caused by the quasi-steady fluid forcing. The large-amplitude flapping motion is observed to appear at a constant critical flow speed that is independent of angle of attack. Its characteristics match those of the large-amplitude vortex-induced vibration present at zero angle of attack. The flow speed at which the plate enters the deflected regime decreases linearly as the angle of attack is increased, causing the flapping motion to disappear for angles of attack greater than α≈28∘. Finally, the effect of aspect ratio on the plate dynamics is considered, with reduced aspect ratio plates being shown to lack sharp distinctions between regimes.
BibTeX:
@misc{Huertas-CerdeiraGozaSaderEtAl2020,
  author = {Cecilia Huertas-Cerdeira and Andres Goza and John E. Sader and Tim Colonius and Morteza Gharib},
  title = {Dynamics of an inverted cantilever plate at moderate angle of attack},
  year = {2020},
  url = {https://arxiv.org/abs/2005.07374}
}
Kamal, O., Rigas, G., Lakebrink, M.T. and Colonius, T. Application of the One-way Navier-Stokes equations to hypersonic boundary layers 2020 AIAA Aviation 2020 Forum  DOI URL 
Abstract: Prediction of linear amplification of disturbances in hypersonic boundary layers is challenging due to the presence and interactions of discrete modes (e.g. Tollmien-Schlichting and Mack) and continuous modes (entropic, vortical, and acoustic). While DNS and global analysis can be used, the large grids required make the computation of optimal transient and forced responses expensive, particularly when a large parameter space is required. At the same time, parabolized stability equations are non-convergent and unreliable for problems involving multi-modal and non-modal interactions. In this work, we apply the One-Way Navier-Stokes (OWNS) equations to hypersonic boundary layers. OWNS is based on a rigorous, approximate parabolization of the equations of motion that removes disturbances with upstream group velocity using a high-order recursive filter. We extend the original algorithm by considering non-orthogonal body-fitted curvilinear coordinates and incorporate full compressibility with temperature-dependent fluid properties. We validate the results by comparing to DNS data for a flat plate and sharp cone, and to LST results for local disturbances on the centerline of the HIFiRE-5 elliptic cone. OWNS provides DNS-quality results for the former flows at a small fraction of the computational expense.
BibTeX:
@inproceedings{KamalRigasLakebrinkEtAl2020,
  author = {Kamal, Omar and Rigas, Georgios and Lakebrink, Matthew T. and Colonius, T.},
  title = {Application of the One-way Navier-Stokes equations to hypersonic boundary layers},
  booktitle = {AIAA Aviation 2020 Forum},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2020},
  url = {http://colonius.caltech.edu/pdfs/KamalRigasLakebrinkEtAl2020.pdf},
  doi = {https://doi.org/10.2514/6.2020-2986}
}
Karban, U., Bugeat, B., Martini, E., Towne, A., Cavalieri, A., Lesshafft, L., Agarwal, A., Jordan, P. and Colonius, T. Ambiguity in mean-flow-based linear analysis 2020 Journal of Fluid Mechanics
Vol. 900, pp. R5 
DOI URL 
Abstract: Linearisation of the Navier-Stokes equations about the mean of a turbulent flow forms the foundation of popular models for energy amplification and coherent structures, including resolvent analysis. While the Navier-Stokes equations can be equivalently written using many different sets of dependent variables, we show that the properties of the linear operator obtained via linearisation about the mean depend on the variables in which the equations are written prior to linearisation, and can be modified under nonlinear transformation of variables. For example, we show that using primitive and conservative variables leads to differences in the singular values and modes of the resolvent operator for turbulent jets, and that the differences become more severe as variable-density effects increase. This lack of uniqueness of mean-flow-based linear analysis provides new opportunities for optimising models by specific choice of variables while also highlighting the importance of carefully accounting for the nonlinear terms that act as a forcing on the resolvent operator.
BibTeX:
@article{KarbanBugeatMartiniEtAl2020,
  author = {Karban, U and Bugeat, B and Martini, E and Towne, A and Cavalieri, A.V.G. and Lesshafft, L. and Agarwal, A and Jordan, P and Colonius, T.},
  title = {Ambiguity in mean-flow-based linear analysis},
  journal = {Journal of Fluid Mechanics},
  year = {2020},
  volume = {900},
  pages = {R5},
  url = {https://arxiv.org/abs/2005.05703},
  doi = {https://doi.org/10.1017/jfm.2020.566}
}
Ke, Y., Colonius, T., Pullin, D. and Winckelmans, G. Dynamics and decay of a spherical region of turbulence in free space 2020 Journal of Fluid Mechanics
Vol. 907, pp. A19 
DOI URL 
Abstract: We perform direct numerical simulation and large-eddy simulation of an initially spherical region of turbulence evolving in free space. The computations are performed with a lattice Green's function method, which allows the exact free-space boundary conditions to be imposed on a compact vortical region. Large-eddy simulations are conducted with the stretched vortex subgrid stress model. The initial condition is spherically windowed, isotropic homogeneous incompressible turbulence. We study the spectrum and statistics of the decaying turbulence and compare the results with decaying isotropic turbulence, including cases representing different low-wavenumber behaviour of the energy spectrum (i.e. k(2) versus k(4)). At late times the turbulent sphere expands with both mean radius and integral scale showing similar timewise growth exponents. The low-wavenumber behaviour has little effect on the inertial scales, and we find that decay rates follow the predictions of Saffman (J. Fluid Mech., vol. 27, 1967, pp. 581-593) in both cases, at least until approximately 400 initial eddy turnover times. The boundary of the spherical region develops intermittency and features ejections of vortex rings. These are shown to occur at the integral scale of the initial turbulence field and are hypothesized to occur due to a local imbalance of impulse on this scale.
BibTeX:
@article{KeColoniusPullinEtAl2020,
  author = {Ke, Yu and Colonius, Tim and Pullin, D.I. and Winckelmans, Gregoire},
  title = {Dynamics and decay of a spherical region of turbulence in free space},
  journal = {Journal of Fluid Mechanics},
  year = {2020},
  volume = {907},
  pages = {A19},
  url = {https://arxiv.org/abs/2009.10364},
  doi = {https://doi.org/10.1017/jfm.2020.818}
}
Mancia, L., Yang, J., Spratt, J.-S., Sukovich, J.R., Xu, Z., Colonius, T., Franck, C. and Johnsen, E. Acoustic Cavitation Rheometry 2020 arXiv:2011.11174  URL 
Abstract: Characterization of soft materials is challenging due to their high compliance and the strain-rate dependence of their mechanical properties. The inertial microcavitation-based high strain-rate rheometry (IMR) method [Estrada et al., J. Mech. Phys. Solids, 2018, 112, 291-317] combines laser-induced cavitation measurements with a model for the bubble dynamics to measure local properties of polyacrylamide hydrogel under high strain-rates from 103 to 108 s−1. While promising, laser-induced cavitation involves plasma formation and optical breakdown during nucleation, a process that could alter local material properties before measurements are obtained. In the present study, we extend the IMR method to another means to generate cavitation, namely high-amplitude focused ultrasound, and apply the resulting acoustic-cavitation-based IMR to characterize the mechanical properties of agarose hydrogels. Material properties including viscosity, elastic constants, and a stress-free bubble radius are inferred from bubble radius histories in 0.3% and 1
% agarose gels. An ensemble-based data assimilation is used to further help interpret the obtained estimates. The resulting parameter distributions are consistent with available measurements of agarose gel properties and with expected trends related to gel concentration and high strain-rate loading. Our findings demonstrate the utility of applying IMR and data assimilation methods with single-bubble acoustic cavitation data for measurement of viscoelastic properties.
BibTeX:
@misc{ManciaYangSprattEtAl2020,
  author = {Lauren Mancia and Jin Yang and Jean-Sebastien Spratt and Jonathan R. Sukovich and Zhen Xu and Tim Colonius and Christian Franck and Eric Johnsen},
  title = {Acoustic Cavitation Rheometry},
  year = {2020},
  url = {https://arxiv.org/abs/2011.11174}
}
Pickering, E., Rigas, G., Nogueira Petornio, A.S., Cavalieri, A.V., Schmid, O.T. and Colonius, T. Lift-up, Kelvin-Helmholtz and Orr mechanisms in turbulent jets 2020 Journal of Fluid Mechanics
Vol. 896, pp. A2 
DOI URL 
Abstract: Three amplification mechanisms present in turbulent jets, namely lift-up, Kelvin-Helmholtz and Orr, are characterized via global resolvent analysis and spectral proper orthogonal decomposition (SPOD) over a range of Mach numbers. The lift-up mechanism was recently identified in turbulent jets via local analysis by Nogueira et al. (J. Fluid Mech., vol. 873, 2019, pp. 211-237) at low Strouhal number () and non-zero azimuthal wavenumbers (). In these limits, a global SPOD analysis of data from high-fidelity simulations reveals streamwise vortices and streaks similar to those found in turbulent wall-bounded flows. These structures are in qualitative agreement with the global resolvent analysis, which shows that they are a response to upstream forcing of streamwise vorticity near the nozzle exit. Analysis of mode shapes, component-wise amplitudes and sensitivity analysis distinguishes the three mechanisms and the regions of frequency-wavenumber space where each dominates, finding lift-up to be dominant as . Finally, SPOD and resolvent analyses of localized regions show that the lift-up mechanism is present throughout the jet, with a dominant azimuthal wavenumber inversely proportional to streamwise distance from the nozzle, with streaks of azimuthal wavenumber exceeding five near the nozzle, and wavenumbers one and two most energetic far downstream of the potential core.
BibTeX:
@article{PickeringRigasNogueiraEtAl2020,
  author = {Pickering, Ethan and Rigas, Georgios and Nogueira Petornio A.S. and Cavalieri, André V.G. and Schmid, Oliver T. and Colonius, Tim},
  title = {Lift-up, Kelvin-Helmholtz and Orr mechanisms in turbulent jets},
  journal = {Journal of Fluid Mechanics},
  year = {2020},
  volume = {896},
  pages = {A2},
  url = {https://arxiv.org/abs/1909.09737},
  doi = {https://doi.org/10.1017/jfm.2020.301}
}
Pickering, E., Rigas, G., Schmidt, O.T., Sipp, D. and Colonius, T. Optimal eddy viscosity for resolvent-based models of coherent structures in turbulent jets 2020 arXiv:2005.10964  URL 
BibTeX:
@misc{PickeringRigasSchnidtEtAl2020,
  author = {Ethan Pickering and Georgios Rigas and Oliver T. Schmidt and Denis Sipp and Tim Colonius},
  title = {Optimal eddy viscosity for resolvent-based models of coherent structures in turbulent jets},
  year = {2020},
  url = {https://arxiv.org/abs/2005.10964}
}
Pickering, E.M., Towne, A., Jordan, P. and Colonius, T. Resolvent-based jet noise models: a projection approach 2020 AIAA Scitech 2020 Forum  DOI URL 
BibTeX:
@inproceedings{PickeringTowneJordanEtAl2020,
  author = {Pickering, Ethan M and Towne, Aaron and Jordan, Peter and Colonius, Tim},
  title = {Resolvent-based jet noise models: a projection approach},
  booktitle = {AIAA Scitech 2020 Forum},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2020},
  url = {http://colonius.caltech.edu/pdfs/PickeringTowneJordanEtAl2020.pdf},
  doi = {https://doi.org/10.2514/6.2020-0999}
}
Rigas, G., Sipp, D. and Colonius, T. Non-linear input/output analysis: application to boundary layer transition 2020 arXiv:2001.09440  URL 
Abstract: The impact of a collapsing gas bubble above rigid, notched walls is considered. Such surface crevices and imperfections often function as bubble nucleation sites, and thus have a direct relation to cavitation-induced erosion and damage structures. A generic configuration is investigated numerically using a second-order-accurate compressible multi-component flow solver in a two-dimensional axisymmetric coordinate system. Results show that the crevice geometry has a significant effect on the collapse dynamics, jet formation, subsequent wave dynamics, and interactions. The wall-pressure distribution associated with erosion potential is a direct consequence of development and intensity of these flow phenomena.
BibTeX:
@misc{RigasSippColonius2020,
  author = {Georgios Rigas and Denis Sipp and Tim Colonius},
  title = {Non-linear input/output analysis: application to boundary layer transition},
  year = {2020},
  url = {https://arxiv.org/abs/2001.09440}
}
Schmidmayer, K., Bryngelson, S. and Colonius, T. An assessment of multicomponent flow models and interface capturing schemes for spherical bubble dynamics 2020 Journal of Computational Physics
Vol. 402, pp. 109080 
DOI URL 
Abstract: Numerical simulation of bubble dynamics and cavitation is challenging; even the seemingly simple problem of a collapsing spherical bubble is difficult to compute accurately with a general, three-dimensional, compressible, multicomponent flow solver. Difficulties arise due to both the physical model and the numerical method chosen for its solution. We consider the 5-equation model of Allaire et al. [1] and Massoni et al. [2], the 5-equation model of Kapila et al. [3], and the 6-equation model of Saurel et al. [4] as candidate approaches for spherical bubble dynamics, and both MUSCL and WENO interface-capturing methods are implemented and compared. We demonstrate the inadequacy of the traditional 5-equation model for spherical bubble collapse problems and explain the corresponding advantages of the augmented model of Kapila et al. [3] for representing this phenomenon. Quantitative comparisons between the augmented 5-equation and 6-equation models for three-dimensional bubble collapse problems demonstrate the versatility of the pressure-disequilibrium model. Lastly, the performance of the pressure-disequilibrium model for representing a three-dimensional spherical bubble collapse for different bubble interior/exterior pressure ratios is evaluated for different numerical methods. Pathologies associated with each factor and their origins are identified and discussed.
BibTeX:
@article{SchmidmayerBryngelsonColonius2020,
  author = {Schmidmayer, K. and Bryngelson, S.H. and Colonius, T.},
  title = {An assessment of multicomponent flow models and interface capturing schemes for spherical bubble dynamics},
  journal = {Journal of Computational Physics},
  year = {2020},
  volume = {402},
  pages = {109080},
  url = {https://arxiv.org/abs/1903.08242},
  doi = {https://doi.org/10.1016/j.jcp.2019.109080}
}
Schmidt, O.T. and Colonius, T. Guide to Spectral Proper Orthogonal Decomposition 2020 AIAA Journal
Vol. 58(3), pp. 1023-1033 
DOI URL 
Abstract: This paper discusses the spectral proper orthogonal decomposition and its use in identifying modes, or structures, in flow data. A specific algorithm based on estimating the cross-spectral density tensor with Welch's method is presented, and guidance is provided on selecting data sampling parameters and understanding tradeoffs among them in terms of bias, variability, aliasing, and leakage. Practical implementation issues, including dealing with large datasets, are discussed and illustrated with examples involving experimental and computational turbulent flow data.
BibTeX:
@article{SchmidtColonius2020,
  author = {Oliver T. Schmidt and Tim Colonius},
  title = {Guide to Spectral Proper Orthogonal Decomposition},
  journal = {AIAA Journal},
  year = {2020},
  volume = {58},
  number = {3},
  pages = {1023--1033},
  url = {htttps://colonius.caltech.edu/pdfs/SchmidtColonius2020.pdf},
  doi = {https://doi.org/10.2514/1.J058809}
}
da Silva, A.F.C. and Colonius, T. Flow state estimation in the presence of discretization errors 2020 Journal of Fluid Mechanics
Vol. 890 
DOI URL 
Abstract: Ensemble data assimilation methods integrate measurement data and computational flow models to estimate the state of fluid systems in a robust, scalable way. However, discretization errors in the dynamical and observation models lead to biased forecasts and poor estimator performance. We propose a low-rank representation for this bias, whose dynamics is modelled by data-informed, time-correlated processes. State and bias parameters are simultaneously corrected online with the ensemble Kalman filter. The proposed methodology is then applied to the problem of estimating the state of a two-dimensional flow at modest Reynolds number using an ensemble of coarse-mesh simulations and pressure measurements at the surface of an immersed body in a synthetic experiment framework. Using an ensemble size of 60, the bias-aware estimator is demonstrated to achieve at least 70 % error reduction when compared to its bias-blind counterpart. Strategies to determine the bias statistics and their impact on the estimator performance are discussed.
BibTeX:
@article{DaSilvaColonius2020,
  author = {Andre F. C. da Silva and Tim Colonius},
  title = {Flow state estimation in the presence of discretization errors},
  journal = {Journal of Fluid Mechanics},
  year = {2020},
  volume = {890},
  url = {https://colonius.caltech.edu/pdfs/DaSilvaColonius2020.pdf},
  doi = {https://doi.org/10.1017/jfm.2020.103}
}
Spratt, J.-S., Rodriguez, M., Schmidmayer, K., Bryngelson, S., Yang, J., Franck, C. and Colonius, T. Characterizing viscoelastic materials via ensemble-based data assimilation of bubble collapse observations 2020 arXiv:2008.04410  URL 
Abstract: Viscoelastic material properties at high strain rates are needed to model many biological and medical systems. Bubble cavitation can induce such strain rates, and the resulting bubble dynamics are sensitive to the material properties. Thus, in principle, these properties can be inferred via measurements of the bubble dynamics. Estrada et al. (2018) demonstrated such bubble-dynamic high-strain-rate rheometry by using least-squares shooting to minimize the difference between simulated and experimental bubble radius histories. We generalize their technique to account for additional uncertainties in the model, initial conditions, and material properties needed to uniquely simulate the bubble dynamics. Ensemble-based data assimilation minimizes the computational expense associated with the bubble cavitation model. We test an ensemble Kalman filter (EnKF), an iterative ensemble Kalman smoother (IEnKS), and a hybrid ensemble-based 4D--Var method (En4D--Var) on synthetic data, assessing their estimations of the viscosity and shear modulus of a Kelvin--Voigt material. Results show that En4D--Var and IEnKS provide better moduli estimates than EnKF. Applying these methods to the experimental data of Estrada et al. (2018) yields similar material property estimates to those they obtained, but provides additional information about uncertainties. In particular, the En4D--Var yields lower viscosity estimates for some experiments, and the dynamic estimators reveal a potential mechanism that is unaccounted for in the model, whereby the viscosity is reduced in some cases due to material damage occurring at bubble collapse.
BibTeX:
@misc{SprattRodriguezSchmidmayerEtAl2020,
  author = {Jean-Sebastien Spratt and Mauro Rodriguez and Kevin Schmidmayer and Spencer Bryngelson and Jin Yang and Christian Franck and Tim Colonius},
  title = {Characterizing viscoelastic materials via ensemble-based data assimilation of bubble collapse observations},
  year = {2020},
  url = {https://arxiv.org/abs/2008.04410}
}
Stevens, B. and Colonius, T. Enhancement of shock-capturing methods via machine learning 2020 Theoretical and Computational Fluid Dynamics
Vol. 34(4), pp. 483-496 
DOI URL 
Abstract: In recent years, machine learning has been used to create data-driven solutions to problems for which an algorithmic solution is intractable, as well as fine-tuning existing algorithms. This research applies machine learning to the development of an improved finite-volume method for simulating PDEs with discontinuous solutions. Shock-capturing methods make use of nonlinear switching functions that are not guaranteed to be optimal. Because data can be used to learn nonlinear relationships, we train a neural network to improve the results of a fifth-order WENO method. We post-process the outputs of the neural network to guarantee that the method is consistent. The training data consist of the exact mapping between cell averages and interpolated values for a set of integrable functions that represent waveforms we would expect to see while simulating a PDE. We demonstrate our method on linear advection of a discontinuous function, the inviscid Burgers' equation, and the 1-D Euler equations. For the latter, we examine the Shu-Osher model problem for turbulence-shock wave interactions. We find that our method outperforms WENO in simulations where the numerical solution becomes overly diffused due to numerical viscosity.
BibTeX:
@article{StevensColonius2020,
  author = {Stevens, Ben and Colonius, Tim},
  title = {Enhancement of shock-capturing methods via machine learning},
  journal = {Theoretical and Computational Fluid Dynamics},
  year = {2020},
  volume = {34},
  number = {4},
  pages = {483-496},
  url = {https://arxiv.org/abs/2002.02521},
  doi = {https://doi.org/10.1007/s00162-020-00531-1}
}
Stevens, B. and Colonius, T. FiniteNet: A Fully Convolutional LSTM Network Architecture for Time-Dependent Partial Differential Equations 2020 arXiv:2002.03014  URL 
Abstract: In this work, we present a machine learning approach for reducing the error when numerically solving time-dependent partial differential equations (PDE). We use a fully convolutional LSTM network to exploit the spatiotemporal dynamics of PDEs. The neural network serves to enhance finite-difference and finite-volume methods (FDM/FVM) that are commonly used to solve PDEs, allowing us to maintain guarantees on the order of convergence of our method. We train the network on simulation data, and show that our network can reduce error by a factor of 2 to 3 compared to the baseline algorithms. We demonstrate our method on three PDEs that each feature qualitatively different dynamics. We look at the linear advection equation, which propagates its initial conditions at a constant speed, the inviscid Burgers' equation, which develops shockwaves, and the Kuramoto-Sivashinsky (KS) equation, which is chaotic.
BibTeX:
@misc{StevensColonius2020b,
  author = {Ben Stevens and Tim Colonius},
  title = {FiniteNet: A Fully Convolutional LSTM Network Architecture for Time-Dependent Partial Differential Equations},
  year = {2020},
  url = {https://arxiv.org/abs/2002.03014}
}
Tosi, L.P., Dorschner, B. and Colonius, T. Flutter Instability in an Internal Flow Energy Harvester 2020 arXiv:2010.04037  URL 
Abstract: Vibration-based flow energy harvesting enables robust, in-situ energy extraction for low-power applications, such as distributed sensor networks. Fluid-structure instabilities dictate a harvester's viability since the structural response to the flow determines its power output. Previous work on a flextensional-based flow energy harvester demonstrated that an elastic member within a converging-diverging channel is susceptible to the aeroelastic flutter. This work explores the mechanism driving flutter through experiments and simulations. A model is then developed based on channel flow-rate modulation and considering the effects of both normal and spanwise flow confinement on the instability. Linear stability analysis of the model replicates flutter onset, critical frequency, and mode shapes observed in experiments. The model suggests that flow modulation through the channel throat is the principal mechanism for the fluid-induced vibration. The generalized model presented can serve as the foundation of design parameter exploration for energy harvesters, perhaps leading to more powerful devices in the future, but also to other similar flow geometries where the flutter instability arises in an elastic member within a narrow flow passage.
BibTeX:
@misc{TosiDorschnerColonius2020,
  author = {L. P. Tosi and B. Dorschner and T. Colonius},
  title = {Flutter Instability in an Internal Flow Energy Harvester},
  year = {2020},
  url = {https://arxiv.org/abs/2010.04037}
}
Trummler, T., Bryngelson, S.H., Schmidmayer, K., Schmidt, S.J., Colonius, T. and Adams, N.A. Near-surface dynamics of a gas bubble collapsing above a crevice 2020 Journal of Fluid Mechanics
Vol. 899, pp. A16 
DOI URL 
Abstract: The impact of a collapsing gas bubble above rigid, notched walls is considered. Such surface crevices and imperfections often function as bubble nucleation sites, and thus have a direct relation to cavitation-induced erosion and damage structures. A generic configuration is investigated numerically using a second-order accurate compressible multi-component flow solver in a two-dimensional axisymmetric coordinate system. Results show that the crevice geometry has a significant effect on the collapse dynamics, jet formation, subsequent wave dynamics and interactions. The wall-pressure distribution associated with erosion potential is a direct consequence of development and intensity of these flow phenomena.
BibTeX:
@article{TrummlerBrungelsonSchmidmayerEtAl2020,
  author = {Trummler, Theresa and Bryngelson, Spencer H. and Schmidmayer, Kevin and Schmidt, Steffen J. and Colonius, T. and Adams, Nikolaus A.},
  title = {Near-surface dynamics of a gas bubble collapsing above a crevice},
  journal = {Journal of Fluid Mechanics},
  year = {2020},
  volume = {899},
  pages = {A16},
  url = {https://arxiv.org/abs/1912.07022},
  doi = {https://doi.org/10.1017/jfm.2020.432}
}
Yu, K., Dorschner, B. and Colonius, T. Multi-resolution lattice Green's function method for incompressible flows 2020 arXiv:2010:13213  URL 
Abstract: We propose a multi-resolution strategy that is compatible with the lattice Green's function (LGF) technique for solving viscous, incompressible flows on unbounded domains. The LGF method exploits the regularity of a finite-volume scheme on a formally unbounded Cartesian mesh to yield robust and computationally efficient solutions. The original method is spatially adaptive, but challenging to integrate with embedded mesh refinement as the underlying LGF is only defined for a fixed resolution. We present an ansatz for adaptive mesh refinement, where the solutions to the pressure Poisson equation are approximated using the LGF technique on a composite mesh constructed from a series of infinite lattices of differing resolution. To solve the incompressible Navier-Stokes equations, this is further combined with an integrating factor for the viscous terms and an appropriate Runge-Kutta scheme for the resulting differential-algebraic equations. The parallelized algorithm is verified through with numerical simulations of vortex rings, and the collision of vortex rings at high Reynolds number is simulated to demonstrate the reduction in computational cells achievable with both spatial and refinement adaptivity.
BibTeX:
@misc{YuDorschnerColonius2020,
  author = {Ke Yu and Benedikt Dorschner and Tim Colonius},
  title = {Multi-resolution lattice Green's function method for incompressible flows},
  year = {2020},
  url = {https://arxiv.org/abs/2010.13213}
}
Bryngelson, S. and Colonius, T. Annular and spiral bubble nets: A simulation-focused analysis of humpback whale feeding strategies 2019 178th Meeting of the Acoustical Society of America  DOI  
BibTeX:
@inproceedings{BryngelsonColonius2019a,
  author = {Bryngelson, S.H. and Colonius, T.},
  title = {Annular and spiral bubble nets: A simulation-focused analysis of humpback whale feeding strategies},
  booktitle = {178th Meeting of the Acoustical Society of America},
  year = {2019},
  doi = {https://doi.org/10.1121/1.5136599}
}
Bryngelson, S.H. and Colonius, T. A comparison of ensemble- and volume-averaged bubbly flow models 2019 10th International Conference on Multiphase Flow, Rio de Janeiro, Brazil  URL 
BibTeX:
@inproceedings{BryngelsonColonius2019,
  author = {Bryngelson, S. H. and Colonius, T.},
  title = {A comparison of ensemble- and volume-averaged bubbly flow models},
  booktitle = {10th International Conference on Multiphase Flow, Rio de Janeiro, Brazil},
  year = {2019},
  url = {http://colonius.caltech.edu/pdfs/BryngelsonColonius2019.pdf}
}
Bryngelson, S.H., Schmidmayer, K. and Colonius, T. A quantitative comparison of phase-averaged models for bubbly, cavitating flows 2019 International Journal of Multiphase Flow
Vol. 115, pp. 137-143 
DOI URL 
Abstract: We compare the computational performance of two modeling approaches for the flow of dilute cavitation bubbles in a liquid. The first approach is a deterministic model, for which bubbles are represented in a Lagrangian framework as advected features, each sampled from a distribution of equilibrium bubble sizes. The dynamic coupling to the liquid phase is modeled through local volume averaging. The second approach is stochastic; ensemble-phase averaging is used to derive mixture-averaged equations and field equations for the associated bubble properties are evolved in an Eulerian reference frame. For polydisperse mixtures, the probability density function of the equilibrium bubble radii is discretized and bubble properties are solved for each representative bin. In both cases, the equations are closed by solving Rayleigh-Plesset-like equations for the bubble dynamics as forced by the local or mixture-averaged pressure, respectively. An acoustically excited dilute bubble screen is used as a case study for comparisons. We show that observables of ensemble-and volume-averaged simulations match closely and that their convergence is first order under grid refinement. Guidelines are established for phase-averaged simulations by comparing the computational costs of methods. The primary costs are shown to be associated with stochastic closure; polydisperse ensemble-averaging requires many samples of the underlying PDF and volume-averaging requires repeated, randomized simulations to accurately represent a homogeneous bubble population. The relative sensitivities of these costs to spatial resolution and bubble void fraction are presented.
BibTeX:
@article{BryngelsonSchmidmayerColonius2019,
  author = {Bryngelson, S. H. and Schmidmayer, K. and Colonius, T.},
  title = {A quantitative comparison of phase-averaged models for bubbly, cavitating flows},
  journal = {International Journal of Multiphase Flow},
  year = {2019},
  volume = {115},
  pages = {137--143},
  url = {http://colonius.caltech.edu/pdfs/BryngelsonSchmidmayerColonius2019.pdf},
  doi = {https://doi.org/10.1016/j.ijmultiphaseflow.2019.03.028}
}
Bryngelson, S.H., Schmidmayer, K., Coralic, V., Meng, J.C., Maeda, K. and Colonius, T. MFC: An open-source high-order multi-component, multi-phase, and multi-scale compressible flow solver 2019 arXiv:1907.10512  URL 
Abstract: MFC is an open-source tool for solving multi-component, multi-phase, and bubbly compressible flows. It is capable of efficiently solving a wide range of flows, including droplet atomization, shock-bubble interaction, and gas bubble cavitation. We present the 5- and 6-equation thermodynamically-consistent diffuse-interface models we use to handle such flows, which are coupled to high-order interface-capturing methods, HLL-type Riemann solvers, and TVD time-integration schemes that are capable of simulating unsteady flows with strong shocks. The numerical methods are implemented in a flexible, modular framework that is amenable to future development. The methods we employ are validated via comparisons to experimental results for shock-bubble, shock-droplet, and shock-water-cylinder interaction problems and verified to be free of spurious oscillations for material-interface advection and gas-liquid Riemann problems. For smooth solutions, such as the advection of an isentropic vortex, the methods are verified to be high-order accurate. Illustrative examples involving shock-bubble-vessel-wall and acoustic-bubble-net interactions are used to demonstrate the full capabilities of MFC.
BibTeX:
@misc{BryngelsonSchmidmayerCoralicEtAl2019,
  author = {Bryngelson, Spencer H and Schmidmayer, Kevin and Coralic, Vedran and Meng, Jomela C and Maeda, Kazuki and Colonius, Tim},
  title = {MFC: An open-source high-order multi-component, multi-phase, and multi-scale compressible flow solver},
  year = {2019},
  url = {http://colonius.caltech.edu/pdfs/BryngelsonSchmidmayerCoralicEtAl2019.pdf}
}
Lajús, F., Sinha, A., Cavalieri, A., Deschamps, C. and Colonius, T. Spatial stability analysis of subsonic corrugated jets 2019 Journal of Fluid Mechanics
Vol. 876, pp. 766-791 
DOI URL 
Abstract: The linear stability of high-Reynolds-number corrugated jets is investigated by solving the compressible Rayleigh equation linearized about the time-averaged flow field. A Floquet ansatz is used to account for periodicity of this base flow in the azimuthal direction. The origin of multiple unstable solutions, which are known to appear in these non-circular configurations, is traced through gradual perturbations of a parametrized base-flow profile. It is shown that all unstable modes are corrugated jet continuations of the classical Kelvin-Helmholtz modes of circular jets, highlighting that the same instability mechanism, modified by corrugations, leads to the growth of disturbances in such flows. It is found that under certain conditions the eigenvalues may form saddles in the complex plane and display axis switching in their eigenfunctions. A parametric study is also conducted to understand how penetration and number of corrugations impact stability. The effect of these geometric properties on growth rates and phase speeds of the multiple unstable modes is explored, and the results provide guidelines for the development of nozzle configurations that more effectively modify the Kelvin-Helmholtz instability.
BibTeX:
@article{LajusSinhaCavalieriEtAl2019,
  author = {Lajús, F.C. and Sinha, A. and Cavalieri, A.V.G. and Deschamps, C.J. and Colonius, T.},
  title = {Spatial stability analysis of subsonic corrugated jets},
  journal = {Journal of Fluid Mechanics},
  year = {2019},
  volume = {876},
  pages = {766--791},
  url = {http://colonius.caltech.edu/pdfs/LajusSinhaCavalieriEtAl2019.pdf},
  doi = {https://doi.org/10.1017/jfm.2019.573}
}
Maeda, K. and Colonius, T. Bubble cloud dynamics in an ultrasound field 2019 Journal of Fluid Mechanics
Vol. 862, pp. 1105-1134 
DOI URL 
Abstract: The dynamics of bubble clouds induced by high-intensity focused ultrasound is investigated in a regime where the cloud size is similar to the ultrasound wavelength. High-speed images show that the cloud is asymmetric; the bubbles nearest the source grow to a larger radius than the distal ones. Similar structures of bubble clouds are observed in numerical simulations that mimic the laboratory experiment. To elucidate the structure, a parametric study is conducted for plane ultrasound waves with various amplitudes and diffuse clouds with different initial void fractions. Based on an analysis of the kinetic energy of liquid induced by bubble oscillations, a new scaling parameter is introduced to characterize the dynamics. The new parameter generalizes the cloud interaction parameter originally introduced by d'Agostino & Brennen (J. Fluid Mech., vol. 199, 1989, pp. 155-176). The dynamic interaction parameter controls the energy localization and consequent anisotropy of the cloud. Moreover, the amplitude of the far-field, bubble-scattered acoustics is likewise correlated with the proposed parameter. Findings of the present study not only shed light on the physics of cloud cavitation, but may also be of use for the quantification of the effects of cavitation on outcomes of ultrasound therapies including high-intensity focused ultrasound-based lithotripsy.
BibTeX:
@article{MaedaColonius2019,
  author = {Maeda, K. and Colonius, T.},
  title = {Bubble cloud dynamics in an ultrasound field},
  journal = {Journal of Fluid Mechanics},
  year = {2019},
  volume = {862},
  pages = {1105--1134},
  url = {http://colonius.caltech.edu/pdfs/MaedaColonius2019.pdf},
  doi = {https://doi.org/10.1017/jfm.2018.968}
}
Nogueira, P.A., Cavalieri, A.V., Schmidt, O.T., Jordan, P., Jaunet, V., Pickering, E., Rigas, G. and Colonius, T. Resolvent-based analysis of streaks in turbulent jets 2019 25th AIAA/CEAS Aeroacoustics Conference  DOI URL 
BibTeX:
@inproceedings{NogueiraCavalieriSchmidtEtAl2019,
  author = {Petrônio A. Nogueira and André V. Cavalieri and Oliver T. Schmidt and Peter Jordan and Vincent Jaunet and Ethan Pickering and Georgios Rigas and Tim Colonius},
  title = {Resolvent-based analysis of streaks in turbulent jets},
  booktitle = {25th AIAA/CEAS Aeroacoustics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2019},
  url = {http://colonius.caltech.edu/pdfs/NogueiraCavalieriSchmidtEtAl2019.pdf},
  doi = {https://doi.org/10.2514/6.2019-2569}
}
Pickering, E. and Colonius, T. Furthering resolvent-based jet noise models 2019 178th Meeting of the Acoustical Society of America  DOI  
BibTeX:
@inproceedings{PickeringColonius2019,
  author = {Pickering, E.M. and Colonius, T.},
  title = {Furthering resolvent-based jet noise models},
  booktitle = {178th Meeting of the Acoustical Society of America},
  year = {2019},
  doi = {https://doi.org/10.1121/1.5137546}
}
Pickering, E.M., Rigas, G., Sipp, D., Schmidt, O.T. and Colonius, T. Eddy viscosity for resolvent-based jet noise models 2019 25th AIAA/CEAS Aeroacoustics Conference  DOI URL 
BibTeX:
@inproceedings{PickeringRigasSippEtAl2019,
  author = {Ethan M. Pickering and Georgios Rigas and Denis Sipp and Oliver T. Schmidt and Tim Colonius},
  title = {Eddy viscosity for resolvent-based jet noise models},
  booktitle = {25th AIAA/CEAS Aeroacoustics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2019},
  url = {http://colonius.caltech.edu/pdfs/PickeringRigasSippEtAl2019.pdf},
  doi = {https://doi.org/10.2514/6.2019-2454}
}
Pishchalnikov, Y.A., Behnke-Parks, W.M., Schmidmayer, K., Maeda, K., Colonius, T., Kenny, T.W. and Laser, D.J. High-speed video microscopy and numerical modeling of bubble dynamics near a surface of urinary stone 2019 Journal of the Acoustical Society of America
Vol. 146(1), pp. 516-531 
DOI URL 
Abstract: Ultra-high-speed video microscopy and numerical modeling were used to assess the dynamics of microbubbles at the surface of urinary stones. Lipid-shell microbubbles designed to accumulate on stone surfaces were driven by bursts of ultrasound in the sub-MHz range with pressure amplitudes on the order of 1 MPa. Microbubbles were observed to undergo repeated cycles of expansion and violent collapse. At maximum expansion, the microbubbles' cross-section resembled an ellipse truncated by the stone. Approximating the bubble shape as an oblate spheroid, this study modeled the collapse by solving the multicomponent Euler equations with a two-dimensional-axisymmetric code with adaptive mesh refinement for fine resolution of the gas-liquid interface. Modeled bubble collapse and high-speed video microscopy showed a distinctive circumferential pinching during the collapse. In the numerical model, this pinching was associated with bidirectional microjetting normal to the rigid surface and toroidal collapse of the bubble. Modeled pressure spikes had amplitudes two-to-three orders of magnitude greater than that of the driving wave. Micro-computed tomography was used to study surface erosion and formation of microcracks from the action of microbubbles. This study suggests that engineered microbubbles enable stone-treatment modalities with driving pressures significantly lower than those required without the microbubbles.
BibTeX:
@article{PishchalnikovBehnkeParksSchmidmayerEtAl2019,
  author = {Pishchalnikov, Yuri A and Behnke-Parks, William M and Schmidmayer, Kevin and Maeda, Kazuki and Colonius, Tim and Kenny, Thomas W and Laser, Daniel J},
  title = {High-speed video microscopy and numerical modeling of bubble dynamics near a surface of urinary stone},
  journal = {Journal of the Acoustical Society of America},
  year = {2019},
  volume = {146},
  number = {1},
  pages = {516--531},
  url = {http://colonius.caltech.edu/pdfs/PishchalnikovBehnkeParksSchmidmayerEtAl2019.pdf},
  doi = {https://doi.org/10.1121/1.5116693}
}
Rigas, G., Pickering, E.M., Schmidt, O.T., Nogueira, P.A., Cavalieri, A.V., Brès, G.A. and Colonius, T. Streaks and coherent structures in jets from round and serrated nozzles 2019 25th AIAA/CEAS Aeroacoustics Conference  DOI URL 
BibTeX:
@inproceedings{RigasPickeringSchmidtEtAl2019,
  author = {Georgios Rigas and Ethan M. Pickering and Oliver T. Schmidt and Petrônio A. Nogueira and André V. Cavalieri and Guillaume A. Brès and Tim Colonius},
  title = {Streaks and coherent structures in jets from round and serrated nozzles},
  booktitle = {25th AIAA/CEAS Aeroacoustics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2019},
  url = {http://colonius.caltech.edu/pdfs/RigasPickeringSchmidtEtAl2019.pdf},
  doi = {https://doi.org/10.2514/6.2019-2597}
}
Schmidmayer, K. and Colonius, T. A comparative study on interface-capturing models and schemes to solve bubble dynamics and cavitation 2019 10th International Conference on Multiphase Flow, Rio de Janeiro, Brazil  URL 
BibTeX:
@inproceedings{SchmidmayerColonius2019,
  author = {Schmidmayer, K. and Colonius, T.},
  title = {A comparative study on interface-capturing models and schemes to solve bubble dynamics and cavitation},
  booktitle = {10th International Conference on Multiphase Flow, Rio de Janeiro, Brazil},
  year = {2019},
  url = {http://colonius.caltech.edu/pdfs/SchmidmayerColonius2019.pdf}
}
da Silva, A.F.C. An EnKF-based Flow State Estimator for Aerodynamic Problems 2019 School: California Institute of Technology  URL 
Abstract: Regardless of the plant model, robust flow estimation based on limited measurements remains a major challenge in successful flow control applications. Aiming to combine the robustness of a high-dimensional representation of the dynamics with the cost efficiency of a low-order approximation of the state covariance matrix, a flow state estimator based on the Ensemble Kalman Filter (EnKF) is applied to two-dimensional flow past a cylinder and an airfoil at high angle of attack and low Reynolds number. For development purposes, we use the numerical algorithm as both the estimator and as a surrogate for the measurements. In a perfect-model framework, a reduced number of either pressure sensors on the surface of the body or sparsely placed velocity probes in the wake are sufficient to accurately estimate the instantaneous flow state. Because the dynamics of these flows are restricted to a low-dimensional manifold of the state space, a small ensemble size is sufficient to yield the correct asymptotic behavior. The relative importance of each sensor location is evaluated by analyzing how they influence the estimated flow field, and optimal locations for pressure sensors are determined.

However, model inaccuracies are ubiquitous in practical applications. Covariance inflation is used to enhance the estimator performance in the presence of unmodeled freestream perturbations. A combination of parametric modeling and augmented state methodology is used to successfully estimate the forces on immersed bodies subjected to deterministic and random gusts. The robustness of high-dimensional representation of the dynamics to the choice of parameters such as the Reynolds number is inherited by the estimator, which was shown to successfully estimate the reference Reynolds number on the fly. Spatial and temporal discretization can constitute a second source of errors which can render numerical solutions a biased representation of reality. Left unaccounted for, biased forecast and observation models can lead to poor estimator performance. In this work, we propose a low-rank representation for the bias whose dynamics are represented by a colored-noise process. System state and bias parameters are simultaneously tracked online with the Ensemble Kalman Filter (EnKF) algorithm. The proposed methodology is demonstrated to achieve a 70% error reduction for the problem of estimating the state of the two-dimensional low-Re flow past a flat plate at high angle of attack using an ensemble of coarse-mesh simulations and pressure measurements at the surface of the body, compared to a bias-blind estimator. Strategies to determine the bias statistics and to deal with nonlinear observation functions in the context of ensemble methods are discussed.

BibTeX:
@phdthesis{daSilva2019,
  author = {da Silva, A. F. C.},
  title = {An EnKF-based Flow State Estimator for Aerodynamic Problems},
  school = {California Institute of Technology},
  year = {2019},
  url = {http://resolver.caltech.edu/CaltechTHESIS:09072018-105527896}
}
Tosi, L.P. and Colonius, T. Modeling and simulation of a fluttering cantilever in channel flow 2019 Journal of Fluids and Structures
Vol. 89, pp. 174-190 
DOI URL 
Abstract: Characterizing the dynamics of a cantilever in channel flow is relevant to applications ranging from snoring to energy harvesting. Aeroelastic flutter induces large oscillating amplitudes and sharp changes with frequency that impact the operation of these systems, The fluid-structure mechanisms that drive flutter can vary as the system parameters change, with the stability boundary becoming especially sensitive to the channel height and Reynolds number, especially when either or both are small. In this paper, we develop a coupled fluid-structure model for viscous, two-dimensional channel flow of arbitrary shape. Its flutter boundary is then compared to results of two-dimensional direct numerical simulations to explore the model's validity. Provided the non-dimensional channel height remains small, the analysis shows that the model is not only able to replicate DNS results within the parametric limits that ensure the underlying assumptions are met, but also over a wider range of Reynolds numbers and fluid-structure mass ratios. Model predictions also converge toward an inviscid model for the same geometry as Reynolds number increases.
BibTeX:
@article{TosiColonius2019,
  author = {Tosi, L. P. and Colonius, T.},
  title = {Modeling and simulation of a fluttering cantilever in channel flow},
  journal = {Journal of Fluids and Structures},
  year = {2019},
  volume = {89},
  pages = {174-190},
  url = {https://arxiv.org/abs/1903.03298},
  doi = {https://doi.org/10.1016/j.jfluidstructs.2019.02.021}
}
Tosi, L.P.C.F. Fluid-Structure Instability in an Internal Flow Energy Harvester 2019 School: California Institute of Technology  URL 
BibTeX:
@phdthesis{Tosi2019,
  author = {Tosi, L. P. C. F.},
  title = {Fluid-Structure Instability in an Internal Flow Energy Harvester},
  school = {California Institute of Technology},
  year = {2019},
  url = {http://resolver.caltech.edu/CaltechTHESIS:09122018-201219035}
}
Towne, A., Rigas, G. and Colonius, T. A critical assessment of the parabolized stability equations 2019 Theoretical and Computational Fluid Dynamics
Vol. 33(3-4), pp. 359-382 
DOI URL 
Abstract: The parabolized stability equations (PSE) are a ubiquitous tool for studying the stability and evolution of disturbances in weakly nonparallel, convectively unstable flows. The PSE method was introduced as an alternative to asymptotic approaches to these problems. More recently, PSE has been applied with mixed results to a more diverse set of problems, often involving flows with multiple relevant instability modes. This paper investigates the limits of validity of PSE via a spectral analysis of the PSE operator. We show that PSE is capable of accurately capturing only disturbances with a single wavelength at each frequency and that other disturbances are not necessarily damped away or properly evolved, as often assumed. This limitation is the result of regularization techniques that are required to suppress instabilities arising from the ill-posedness of treating a boundary value problem as an initial value problem. These findings are valid for both incompressible and compressible formulations of PSE and are particularly relevant for applications involving multiple modes with different wavelengths and growth rates, such as problems involving multiple instability mechanisms, transient growth, and acoustics. Our theoretical results are illustrated using a generic problem from acoustics and a dual-stream jet, and the PSE solutions are compared to both global solutions of the linearized Navier-Stokes equations and a recently developed alternative parabolization.
BibTeX:
@article{TowneRigasColonius2019,
  author = {Aaron Towne and Georgios Rigas and Tim Colonius},
  title = {A critical assessment of the parabolized stability equations},
  journal = {Theoretical and Computational Fluid Dynamics},
  year = {2019},
  volume = {33},
  number = {3-4},
  pages = {359-382},
  url = {http://colonius.caltech.edu/pdfs/TowneRigasColonius2019.pdf},
  doi = {https://doi.org/10.1007/s00162-019-00498-8}
}
Wilson, C.T., Hall, T.L., Johnsen, E., Mancia, L., Rodriguez, M., Lundt, J., Colonius, T., Henann, D.L., Franck, C., Xu, Z. and Sukovich, J.R. Comparative study of the dynamics of laser and acoustically generated bubbles in viscoelastic media 2019 Physical Review E
Vol. 99(4) 
DOI URL 
Abstract: Experimental observations of the growth and collapse of acoustically and laser-nucleated single bubbles in water and agarose gels of varying stiffness are presented. The maximum radii of generated bubbles decreased as the stiffness of the media increased for both nucleation modalities, but the maximum radii of laser-nucleated bubbles decreased more rapidly than acoustically nucleated bubbles as the gel stiffness increased. For water and low stiffness gels, the collapse times were well predicted by a Rayleigh cavity, but bubbles collapsed faster than predicted in the higher stiffness gels. The growth and collapse phases occurred symmetrically (in time) about the maximum radius in water but not in gels, where the duration of the growth phase decreased more than the collapse phase as gel stiffness increased. Numerical simulations of the bubble dynamics in viscoelastic media showed varying degrees of success in accurately predicting the observations.
BibTeX:
@article{WilsonHallJohnsenEtAl2019,
  author = {Wilson, C. T. and Hall, T. L. and Johnsen, E. and Mancia, L. and Rodriguez, M. and Lundt, J.E. and Colonius, T. and Henann, D. L. and Franck, C. and Xu, Z. and Sukovich, J. R.},
  title = {Comparative study of the dynamics of laser and acoustically generated bubbles in viscoelastic media},
  journal = {Physical Review E},
  year = {2019},
  volume = {99},
  number = {4},
  url = {http://colonius.caltech.edu/pdfs/WilsonHallJohnsenEtAl2019.pdf},
  doi = {https://doi.org/10.1103/PhysRevE.99.043103}
}
Antonialli, L.A., Cavalieri, A., Schmidt, O., Colonius, T., Towne, A., Brès, G.A. and Jordan, P. Amplitude scaling of turbulent-jet wavepackets 2018 2018 AIAA/CEAS Aeroacoustics Conference  DOI URL 
BibTeX:
@inproceedings{AntonialliCavalieriSchmidtEtAl2018,
  author = {Antonialli, Luigi A. and Cavalieri, AndréV. and Schmidt, Oliver and Colonius, Tim and Towne, Aaron and Brès, Guillaume A. and Jordan, Peter},
  title = {Amplitude scaling of turbulent-jet wavepackets},
  booktitle = {2018 AIAA/CEAS Aeroacoustics Conference},
  publisher = {American Institute of Aeronautics and Astronautics (AIAA)},
  year = {2018},
  url = {http://colonius.caltech.edu/pdfs/AntonialliCavalieriSchmidtEtAl2018.pdf},
  doi = {https://doi.org/10.2514/6.2018-2978}
}
Bode, M., Satcunanathan, S., Maeda, K., Colonius, T. and Pitsch, H. An Equation-of-State Tabulation Approach for Injectors with Non-Condensable Gases: Development and Analysis 2018 CAV2018: 10th International Symposium on Cavitation  URL 
BibTeX:
@inproceedings{BodeSatcunanathanMaedaEtAl2018,
  author = {Bode, M. and Satcunanathan, S. and Maeda, K. and Colonius, T. and Pitsch, H.},
  title = {An Equation-of-State Tabulation Approach for Injectors with Non-Condensable Gases: Development and Analysis},
  booktitle = {CAV2018: 10th International Symposium on Cavitation},
  year = {2018},
  url = {http://colonius.caltech.edu/pdfs/BodeSatcunanathanMaedaEtAl2018.pdf}
}
Brès, G.A., Bose, S.T., Emory, M., Ham, F.E., Schmidt, O.T., Rigas, G. and Colonius, T. Large-eddy simulations of co-annular turbulent jet using a Voronoi-based mesh generation framework 2018 2018 AIAA/CEAS Aeroacoustics Conference  DOI URL 
BibTeX:
@inproceedings{BresBoseEmoryEtAl2018,
  author = {Brès, Guillaume A. and Bose, Sanjeeb T. and Emory, Michael and Ham, Frank E. and Schmidt, Oliver T. and Rigas, Georgios and Colonius, Tim},
  title = {Large-eddy simulations of co-annular turbulent jet using a Voronoi-based mesh generation framework},
  booktitle = {2018 AIAA/CEAS Aeroacoustics Conference},
  publisher = {American Institute of Aeronautics and Astronautics (AIAA)},
  year = {2018},
  url = {http://colonius.caltech.edu/pdfs/BresBoseEmoryEtAl2018.pdf},
  doi = {https://doi.org/10.2514/6.2018-3302}
}
Brès, G.A., Jordan, P., Jaunet, V., LeRallic, M., Cavalieri, A.V.G., Towne, A., Lele Sanjiva, K., Colonius, T. and Schmidt, O.T. Importance of the nozzle-exit boundary-layer state in subsonic turbulent jets 2018 Journal of Fluid Mechanics
Vol. 851, pp. 83-124 
DOI URL 
Abstract: To investigate the effects of the nozzle-exit conditions on jet flow and sound fields, large-eddy simulations of an isothermal Mach 0.9 jet issued from a convergent-straight nozzle are performed at a diameter-based Reynolds number of 1 x 10(6). The simulations feature near-wall adaptive mesh refinement, synthetic turbulence and wall modelling inside the nozzle. This leads to fully turbulent nozzle-exit boundary layers and results in significant improvements for the flow field and sound predictions compared with those obtained from the typical approach based on laminar flow in the nozzle. The far-field pressure spectra for the turbulent jet match companion experimental measurements, which use a boundary-layer trip to ensure a turbulent nozzle-exit boundary layer to within 0.5 dB for all relevant angles and frequencies. By contrast, the initially laminar jet results in greater high-frequency noise. For both initially laminar and turbulent jets, decomposition of the radiated noise into azimuthal Fourier modes is performed, and the results show similar azimuthal characteristics for the two jets. The axisymmetric mode is the dominant source of sound at the peak radiation angles and frequencies. The first three azimuthal modes recover more than 97% of the total acoustic energy at these angles and more than 65% (i.e. error less than 2 dB) for all angles. For the main azimuthal modes, linear stability analysis of the near-nozzle mean-velocity profiles is conducted in both jets. The analysis suggests that the differences in radiated noise between the initially laminar and turbulent jets are related to the differences in growth rate of the Kelvin-Helmholtz mode in the near-nozzle region.
BibTeX:
@article{BresJordanJaunetEtAl2018,
  author = {Brès, Guillaume A. and Jordan, Peter and Jaunet, Vincent and LeRallic, Maxime and Cavalieri, André V. G. and Towne, Aaron and Lele Sanjiva K. and Colonius, Tim and Schmidt, Oliver T.},
  title = {Importance of the nozzle-exit boundary-layer state in subsonic turbulent jets},
  journal = {Journal of Fluid Mechanics},
  year = {2018},
  volume = {851},
  pages = {83--124},
  url = {http://colonius.caltech.edu/pdfs/BresJordanJaunetEtAl2018.pdf},
  doi = {https://doi.org/10.1017/jfm.2018.476}
}
Darakananda, D., Eldredge, J., da Silva, A., Colonius, T. and Williams, D.R. EnKF-based Dynamic Estimation of Separated Flows with a Low-Order Vortex Model 2018 56th AIAA Aerospace Sciences Meeting  DOI URL 
BibTeX:
@inproceedings{DarakanandaEldredgeDaSilvaEtAl2018,
  author = {Darwin Darakananda and Jeff Eldredge and Andre da Silva and Tim Colonius and David R. Williams},
  title = {EnKF-based Dynamic Estimation of Separated Flows with a Low-Order Vortex Model},
  booktitle = {56th AIAA Aerospace Sciences Meeting},
  publisher = {American Institute of Aeronautics and Astronautics (AIAA)},
  year = {2018},
  url = {http://colonius.caltech.edu/pdfs/DarakanandaEldredgeDaSilvaEtAl2018.pdf},
  doi = {https://doi.org/10.2514/6.2018-0811}
}
Darakananda, D., da Silva, A., Colonius, T. and Eldredge, J. Data-assimilated low-order vortex modeling of separated flows 2018 Physical Review Fluids
Vol. 3(12), pp. 124701 
DOI URL 
Abstract: Vortex models have been used for decades as computationally efficient tools to investigate unsteady aerodynamics. However, their utility for separated flows particularly when such flows are subjected to incident disturbances has been hindered by the tradeoff between the model's physical fidelity and its expectation for fast prediction (e.g., relative to computational fluid dynamics). In this work, it is shown that physical fidelity and speed can be simultaneously achieved by assimilating measurement data into the model to compensate for unrepresented physics. The underlying inviscid vortex model captures the transport of vortex structures with a standard collection of regularized vortex elements that interact mutually and with an infinitely thin flat plate. In order to maintain a low-dimensional representation, with fewer than O(100) degrees of freedom, an aggregation procedure is developed and utilized in which vortex elements are coalesced at each time step. A flow state vector, composed of vortex element properties as well as the critical leading-edge suction parameter, is advanced within an ensemble Kalman filter (EnKF) framework. In this framework, surface pressure is used to correct the states of an ensemble of randomly initiated vortex models. The overall algorithm is applied to several scenarios of an impulsively started flat plate, in which data from a high-fidelity Navier-Stokes simulation at Reynolds number 500 are used as a surrogate for the measurements. The assimilated vortex model efficiently and accurately predicts the evolving flow as well as the normal force in both the undisturbed case (a separated flow) as well as in the presence of one or more incident gusts, despite lack of a priori knowledge of the gust's characteristics.
BibTeX:
@article{DarakanandaDaSilvaColoniusEtAl2018.pdf,
  author = {Darakananda, D. and da Silva, A.F.C. and Colonius, T. and Eldredge, J.D.},
  title = {Data-assimilated low-order vortex modeling of separated flows},
  journal = {Physical Review Fluids},
  year = {2018},
  volume = {3},
  number = {12},
  pages = {124701},
  url = {http://colonius.caltech.edu/pdfs/DarakanandaDaSilvaColoniusEtAl2018.pdf},
  doi = {https://doi.org/10.1103/physrevfluids.3.124701}
}
Goza, A. Numerical Methods for Fluid-Structure Interaction, and their Application to Flag Flapping 2018 School: California Institute of Technology  URL 
Abstract: This thesis is divided into two parts. Part I is devoted to the development of numerical techniques for simulating fluid-structure interaction (FSI) systems and for educing important physical mechanisms that drive these systems’ behavior; part II discusses the application of many of these techniques to investigate a specific FSI system.

Within part I, we first describe a procedure for accurately computing the stresses on an immersed surface using the immersed-boundary method. This is a key step to simulating FSI problems, as the surface stresses simultaneously dictate the motion of the structure and enforce the no-slip boundary condition on the fluid. At the same time, accurate stress computations are also important for applications involving rigid bodies that are either stationary or moving with prescribed kinematics (e.g., characterizing the performance of wings and aerodynamic bodies in unsteady flows or understanding and controlling flow separation around bluff bodies). Thus, the method is first formulated for the rigid-body prescribed-kinematics case. The procedure described therein is subsequently incorporated into an immersed boundary method for efficiently simulating FSI problems involving arbitrarily large structural motions and rotations.

While these techniques can be used to perform high-fidelity simulations of FSI systems, the resulting data often involves a range of spatial and temporal scales in both the structure and the fluid and are thus typically difficult to interpret directly. The remainder of part I is therefore devoted to extending tools regularly used for understanding complex flows to FSI systems. We focus in particular on the application of global linear stability analysis and snapshot-based data analysis (such as dynamic mode decomposition and proper orthogonal decomposition) to FSI problems. To our knowledge, these techniques had not been applied to deforming-body problems in a manner that that accounts for both the fluid and structure leading up to this work.

Throughout part I, our methods are derived in the context of fairly general FSI systems and are validated using results from the literature for flapping flags in both the conventional configuration (in which the flag is pinned or clamped at its leading edge with respect to the oncoming flow) and the inverted configuration (in which the flag is clamped at its trailing edge). In part II, we apply many of the techniques developed in part I to uncover new physical mechanisms about inverted-flag flapping. We identify the instability-driving mechanism responsible for the initiation of flapping and further characterize the large-amplitude and chaotic flapping regimes that the system undergoes for a range of physical parameters.

BibTeX:
@phdthesis{Goza2018,
  author = {Goza, A.},
  title = {Numerical Methods for Fluid-Structure Interaction, and their Application to Flag Flapping},
  school = {California Institute of Technology},
  year = {2018},
  url = {http://resolver.caltech.edu/CaltechTHESIS:10122017-095438989}
}
Goza, A. and Colonius, T. Modal decomposition of fluid-structure interaction with application to flag flapping 2018 Journal of Fluids and Structures
Vol. 81, pp. 728-737 
DOI URL 
Abstract: Modal decompositions such as proper orthogonal decomposition (POD), dynamic mode decomposition (DMD) and their variants are regularly used to educe physical mechanisms of nonlinear flow phenomena that cannot be easily understood through direct inspection. In fluid-structure interaction (FSI) systems, fluid motion is coupled to vibration and/or deformation of an immersed structure. Despite this coupling, data analysis is often performed using only fluid or structure variables, rather than incorporating both. This approach does not provide information about the manner in which fluid and structure modes are correlated. We present a framework for performing POD and DMD where the fluid and structure are treated together. As part of this framework, we introduce a physically meaningful norm for FSI systems. We first use this combined fluid-structure formulation to identify correlated flow features and structural motions in limit-cycle flag flapping. We then investigate the transition from limit-cycle flapping to chaotic flapping, which can be initiated by increasing the flag mass. Our modal decomposition reveals that at the onset of chaos, the dominant flapping motion increases in amplitude and leads to a bluff-body wake instability. This new bluff-body mode interacts triadically with the dominant flapping motion to produce flapping at the non-integer harmonic frequencies previously reported by Connell and Yue (2007). While our formulation is presented for POD and DMD, there are natural extensions to other data-analysis techniques.
BibTeX:
@article{GozaColonius2018,
  author = {Goza, Andres and Colonius, Tim},
  title = {Modal decomposition of fluid-structure interaction with application to flag flapping},
  journal = {Journal of Fluids and Structures},
  year = {2018},
  volume = {81},
  pages = {728--737},
  url = {http://colonius.caltech.edu/pdfs/GozaColonius2018.pdf},
  doi = {https://doi.org/10.1016/j.jfluidstructs.2018.06.014}
}
Goza, A., Colonius, T. and Sader, J.E. Global modes and nonlinear analysis of inverted-flag flapping 2018 Journal of Fluid Mechanics
Vol. 857, pp. 312-344 
DOI URL 
Abstract: An inverted flag has its trailing edge clamped and exhibits dynamics distinct from that of a conventional flag, whose leading edge is restrained. We perform nonlinear simulations and a global stability analysis of the inverted-flag system for a range of Reynolds numbers, flag masses and stiffnesses. Our global stability analysis is based on a linearisation of the fully coupled fluid-structure system of equations. The calculated equilibria are steady-state solutions of the fully coupled nonlinear equations. By implementing this approach, we (i) explore the mechanisms that initiate flapping, (ii) study the role of vorticity generation and vortex-induced vibration (VIV) in large-amplitude flapping and (iii) characterise the chaotic flapping regime. For point (i), we identify a deformed-equilibrium state and show through a global stability analysis that the onset of small-deflection flapping - where the oscillation amplitude is significantly smaller than in large-amplitude flapping - is due to a supercritical Hopf bifurcation. For large-amplitude flapping, point (ii), we confirm the arguments of Sader et al. (J. Fluid Mech., vol. 793, 2016a) that classical VIV exists when the flag is sufficiently light with respect to the fluid. We also show that for heavier flags, large-amplitude flapping persists (even for Reynolds numbers <50) and is not classical VIV. Finally, with respect to point (iii), chaotic flapping has been observed experimentally for Reynolds numbers of O(10(4)), and here we show that chaos also persists at a moderate Reynolds number of 200. We characterise this chaotic regime and calculate its strange attractor, whose structure is controlled by the above-mentioned deformed equilibria and is similar to a Lorenz attractor.
BibTeX:
@article{GozaColoniusSader2018,
  author = {Goza, Andres and Colonius, Tim and Sader, John Elie},
  title = {Global modes and nonlinear analysis of inverted-flag flapping},
  journal = {Journal of Fluid Mechanics},
  year = {2018},
  volume = {857},
  pages = {312--344},
  url = {http://colonius.caltech.edu/pdfs/GozaColoniusSader2018.pdf},
  doi = {https://doi.org/10.1017/jfm.2018.728}
}
Jardin, T. and Colonius, T. On the lift-optimal aspect ratio of a revolving wing at low Reynolds number 2018 Journal of the Royal Society Interface
Vol. 15(143), pp. 20170933 
DOI URL 
Abstract: Lentink & Dickinson (2009 J. Exp. Biol. 212, 2705-2719. (doi: 10.1242/jeb. 022269)) showed that rotational acceleration stabilized the leading-edge vortex on revolving, low aspect ratio (AR) wings and hypothesized that a Rossby number of around 3, which is achieved during each half-stroke for a variety of hovering insects, seeds and birds, represents a convergent high-lift solution across a range of scales in nature. Subsequent work has verified that, in particular, the Coriolis acceleration plays a key role in LEV stabilization. Implicit in these results is that there exists an optimal AR for wings revolving about their root, because it is otherwise unclear why, apart from possible morphological reasons, the convergent solution would not occur for an even lower Rossby number. We perform direct numerical simulations of the flow past revolving wings where we vary the AR and Rossby numbers independently by displacing the wing root from the axis of rotation. We show that the optimal lift coefficient represents a compromise between competing trends with competing time scales where the coefficient of lift increases monotonically with AR, holding Rossby number constant, but decreases monotonically with Rossby number, when holding AR constant. For wings revolving about their root, this favours wings of AR between 3 and 4.
BibTeX:
@article{JardinColonius2018,
  author = {Jardin, T. and Colonius, T.},
  title = {On the lift-optimal aspect ratio of a revolving wing at low Reynolds number},
  journal = {Journal of the Royal Society Interface},
  year = {2018},
  volume = {15},
  number = {143},
  pages = {20170933},
  url = {http://colonius.caltech.edu/pdfs/JardinColonius2018.pdf},
  doi = {https://doi.org/10.1098/rsif.2017.0933}
}
Jordan, P., Jaunet, V., Towne, A., Cavalieri, A.V., Colonius, T., Schmidt, O. and Agarwal, A. Jet-flap interaction tones 2018 Journal of Fluid Mechanics
Vol. 853, pp. 333-358 
DOI URL 
Abstract: Motivated by the problem of jet-flap interaction noise, we study the tonal dynamics that occurs when an isothermal turbulent jet grazes a sharp edge. We perform hydrodynamic and acoustic pressure measurements to characterise the tones as a function of Mach number and streamwise edge position. The observed distribution of spectral peaks cannot be explained using the usual edge-tone model, in which resonance is underpinned by coupling between downstream-travelling Kelvin- Helmholtz wavepackets and upstream-travelling sound waves. We show, rather, that the strongest tones are due to coupling between Kelvin-Helmholtz wavepackets and a family of trapped, upstream-travelling acoustic modes in the potential core, recently studied by Towne el al. (J. Fluid Mech. vol. 825, 2017) and Schmidt el al. (J. Fluid Mech. vol. 825, 2017). We also study the band-limited nature of the resonance, showing the high-frequency cutoff to be due to the frequency dependence of the upstream-travelling waves. Specifically, at high Mach number, these modes become evanescent above a certain frequency, whereas at low Mach number they become progressively trapped with increasing frequency, which inhibits their reflection in the nozzle plane.
BibTeX:
@article{JordanJaunetTowneEtAl2018,
  author = {Jordan, Peter and Jaunet, Vincent and Towne, Aaron and Cavalieri, André VG and Colonius, Tim and Schmidt, Oliver and Agarwal, Anurag},
  title = {Jet-flap interaction tones},
  journal = {Journal of Fluid Mechanics},
  year = {2018},
  volume = {853},
  pages = {333--358},
  url = {http://colonius.caltech.edu/pdfs/JordanJaunetTowneEtAl2018.pdf},
  doi = {https://doi.org/10.1017/jfm.2018.566}
}
Maeda, K. Simulation, Experiments, and Modeling of Cloud Cavitation with Application to Burst Wave Lithotripsy 2018 School: California Institute of Technology  URL 
Abstract: Simulation, Experiments, and Modeling of Cloud Cavitation with Application to Burst Wave Lithotripsy
Citation
Maeda, Kazuki (2018) Simulation, Experiments, and Modeling of Cloud Cavitation with Application to Burst Wave Lithotripsy. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/N7JK-F529. https://resolver.caltech.edu/CaltechTHESIS:06012018-165819361

Abstract
Modeling, numerical simulations, and experiments are used to investigate the dynamics of cavitation bubble clouds induced by strong ultrasound waves.

A major application of this work is burst wave lithotripsy (BWL), recently proposed method of lithotripsy that uses pulses (typically 10 wavelengths each) of highintensity, focused ultrasound at a frequency of O(100) kHz and an amplitude of O(1) MPa to break kidney stones. BWL is an alternative to standard shockwave lithotripsy (SWL), which uses much higher amplitude shock waves delivered at a typically much lower rate. In both SWL and BWL, the tensile component of the pressure can nucleate cavitation bubbles in the human body. For SWL, cavitation is a significant mechanism in stone communition, but also causes tissue injury. By contrast, little is yet known about cavitation in BWL.

To investigate cloud cavitation in BWL, two numerical tools are developed: a model of ultrasound generation from a medical transducer, and a method of simulating clouds of cavitation bubbles in the focal region of the ultrasound. The numerical tools enable simulation of the cavitation growth and collapse of individual bubbles, their mutual interactions, and the resulting bubble-scattered acoustics. The numerics are implemented in a massively parallel framework to enable large-scale, three-dimensional simulations. Next, the numerical tools are applied to bubble clouds associated with BWL. Additionally, laboratory experiments are conducted in vitro in order to calibrate and validate the simulations. A major feature of the resulting bubble clouds is that the cloud size is similar to the ultrasound wavelength. This results in an anisotropic structure where the bubbles closest to the wave source grow to larger size and oscillate more rapidly. A new scaling parameter is introduced to characterize the nonlinear bubble cloud dynamics that generalizes the cloud interaction parameter of d'Agostino and Brennen (1989) defined for weak (linearized), bubble cloud dynamics excited uniformly by long-wavelength pressure waves. The mechanisms leading to the observed bubble dynamics are identified. The results further show that bubble clouds can scatter a large portion of incident ultrasound and consequently shield distal regions, including kidney stones, from irradiation. This energy shielding is quantified, and the simulations show that even a thin layer of bubbles can scatter up to 90% of the incident wave energy. A strong correlation is identified between the magnitude of energy shielding and the amplitude of the bubble-scattered acoustics. The correlation may be of use to control cavitation in the human body in real time by ultrasound monitoring for better outcomes of BWL.

BibTeX:
@phdthesis{Maeda2018,
  author = {Maeda, K.},
  title = {Simulation, Experiments, and Modeling of Cloud Cavitation with Application to Burst Wave Lithotripsy},
  school = {California Institute of Technology},
  year = {2018},
  url = {http://resolver.caltech.edu/CaltechTHESIS:06012018-165819361}
}
Maeda, K. and Colonius, T. Eulerian-Lagrangian method for simulation of cloud cavitation 2018 Journal of Computational Physics
Vol. 371, pp. 994-1017 
DOI URL 
Abstract: We present a coupled Eulerian-Lagrangian method to simulate cloud cavitation in a compressible liquid. The method is designed to capture the strong, volumetric oscillations of each bubble and the bubble-scattered acoustics. The dynamics of the bubbly mixture is formulated using volume-averaged equations of motion. The continuous phase is discretized on an Eulerian grid and integrated using a high-order, finite-volume weighted essentially non-oscillatory (WENO) scheme, while the gas phase is modeled as spherical, Lagrangian point-bubbles at the sub-grid scale, each of whose radial evolution is tracked by solving the Keller-Miksis equation. The volume of bubbles is mapped onto the Eulerian grid as the void fraction by using a regularization (smearing) kernel. In the most general case, where the bubble distribution is arbitrary, three-dimensional Cartesian grids are used for spatial discretization. In order to reduce the computational cost for problems possessing translational or rotational homogeneities, we spatially average the governing equations along the direction of symmetry and discretize the continuous phase on two-dimensional or axi-symmetric grids, respectively. We specify a regularization kernel that maps the three-dimensional distribution of bubbles onto the field of an averaged two-dimensional or axi-symmetric void fraction. A closure is developed to model the pressure fluctuations at the sub-grid scale as synthetic noise. For the examples considered here, modeling the sub-grid pressure fluctuations as white noise agrees a priori with computed distributions from three-dimensional simulations, and suffices, a posteriori, to accurately reproduce the statistics of the bubble dynamics. The numerical method and its verification are described by considering test cases of the dynamics of a single bubble and cloud cavitation induced by ultrasound fields.
BibTeX:
@article{MaedaColonius2018c,
  author = {Maeda, Kazuki and Colonius, Tim},
  title = {Eulerian-Lagrangian method for simulation of cloud cavitation},
  journal = {Journal of Computational Physics},
  year = {2018},
  volume = {371},
  pages = {994--1017},
  url = {http://colonius.caltech.edu/pdfs/MaedaColonius2018c.pdf},
  doi = {https://doi.org/10.1016/j.jcp.2018.05.029}
}
Maeda, K. and Colonius, T. Numerical Simulation of the Bubble Cloud Dynamics in an Ultrasound Field 2018 CAV2018: 10th International Symposium on Cavitation, Baltimore, MD  URL 
BibTeX:
@inproceedings{MaedaColonius2018b,
  author = {Maeda, K. and Colonius, T.},
  title = {Numerical Simulation of the Bubble Cloud Dynamics in an Ultrasound Field},
  booktitle = {CAV2018: 10th International Symposium on Cavitation, Baltimore, MD},
  year = {2018},
  url = {http://colonius.caltech.edu/pdfs/MaedaColonius2018b.pdf}
}
Maeda, K., Colonius, T., Maxwell, A., Kreider, W. and Bailey, M. Modeling and numerical simulation of the bubble cloud dynamics in an ultrasound field for burst wave lithotripsy 2018 Proceedings of Meetings on Acoustics
Vol. 35, pp. 020006 
DOI URL 
Abstract: Modeling and numerical simulation of bubble clouds induced by intense ultrasound waves are conducted to quantify the effect of cloud cavitation on burst wave lithotripsy, a proposed non-invasive alternative to shock wave lithotripsy that uses pulses of ultrasound with an amplitude of O(1) MPa and a frequency of O(100) kHz. A unidirectional acoustic source model and an Eulerian-Lagrangian method are developed for simulation of ultrasound generation from a multi-element array transducer and cavitation bubbles, respectively. Parametric simulations of the spherical bubble cloud dynamics reveal a new scaling parameter that dictates both the structure of the bubble cloud and the amplitude of the far-field, bubblescattered acoustics. The simulation further shows that a thin layer of bubble clouds nucleated near a kidney stone model can shield up to 90 % of the incoming wave energy, indicating a potential loss of efficacy during the treatment due to cavitation. Strong correlations are identified between the far-field, bubble-scattered acoustics and the magnitude of the shielding, which could be used for ultrasound monitoring of cavitation during treatments. The simulations are validated by companion experiments in vitro.
BibTeX:
@article{MaedaColoniusMaxwellEtAl2018,
  author = {Maeda, K. and Colonius, T. and Maxwell, A. and Kreider, W. and Bailey, M.},
  title = {Modeling and numerical simulation of the bubble cloud dynamics in an ultrasound field for burst wave lithotripsy},
  journal = {Proceedings of Meetings on Acoustics},
  year = {2018},
  volume = {35},
  pages = {020006},
  url = {http://colonius.caltech.edu/pdfs/MaedaColoniusMaxwellEtAl2018.pdf},
  doi = {https://doi.org/10.1121/2.0000946}
}
Maeda, K., Maxwell, A., Colonius, T., Kreider, W. and Bailey, M. Energy shielding by cavitation bubble clouds in burst wave lithotripsy 2018 Journal of the Acoustical Society of America
Vol. 144(5), pp. 2952-2961 
DOI URL 
Abstract: Combined laboratory experiment and numerical simulation are conducted on bubble clouds nucleated on the surface of a model kidney stone to quantify the energy shielding of the stone caused by cavitation during burst wave lithotripsy (BWL). In the experiment, the bubble clouds are visualized and bubble-scattered acoustics are measured. In the simulation, a compressible, multi-component flow solver is used to capture complex interactions among cavitation bubbles, the stone, and the burst wave. Quantitative agreement is confirmed between results of the experiment and the simulation. In the simulation, a significant shielding of incident wave energy by the bubble clouds is quantified. The magnitude of shielding can reach up to 90% of the energy of the incoming burst wave that otherwise would be transmitted into the stone, suggesting a potential loss of efficacy of stone comminution. There is a strong correlation between the magnitude of the energy shielding and the amplitude of the bubble-scattered acoustics, independent of the initial size and the void fraction of the bubble cloud within a range addressed in the simulation. This correlation could provide for real-time monitoring of cavitation activity in BWL.
BibTeX:
@article{MaedaMaxwellColoniusEtAl2018,
  author = {Maeda, K. and Maxwell, A.D. and Colonius, T. and Kreider, W. and Bailey, M.R.},
  title = {Energy shielding by cavitation bubble clouds in burst wave lithotripsy},
  journal = {Journal of the Acoustical Society of America},
  year = {2018},
  volume = {144},
  number = {5},
  pages = {2952--2961},
  url = {http://colonius.caltech.edu/pdfs/MaedaMaxwellColoniusEtAl2018.pdf},
  doi = {https://doi.org/10.1121/1.5079641}
}
Maeda, K., Maxwell, A., Kreider, W., Colonius, T. and Bailey, M. Investigation of the Energy Shielding of Kidney Stones by Cavitation Bubble Clouds during Burst Wave Lithotripsy 2018 CAV2018: 10th International Symposium on Cavitation, Baltimore, MD  URL 
BibTeX:
@inproceedings{MaedaMaxwellKreiderEtAl2018,
  author = {Maeda, K. and Maxwell, A. and Kreider, W. and Colonius, T. and Bailey, M.},
  title = {Investigation of the Energy Shielding of Kidney Stones by Cavitation Bubble Clouds during Burst Wave Lithotripsy},
  booktitle = {CAV2018: 10th International Symposium on Cavitation, Baltimore, MD},
  year = {2018},
  url = {https://arxiv.org/abs/1801.06901}
}
Meng, J.C. and Colonius, T. Numerical simulation of the aerobreakup of a water droplet 2018 Journal of Fluid Mechanics
Vol. 835, pp. 1108-1135 
DOI URL 
Abstract: We present a three-dimensional numerical simulation of the aerobreakup of a spherical water droplet in the flow behind a normal shock wave. The droplet and surrounding gas flow are simulated using the compressible multicomponent Euler equations in a finite-volume scheme with shock and interface capturing. The aerobreakup process is compared with available experimental visualizations. Features of the droplet deformation and breakup in the stripping breakup regime, as well as descriptions of the surrounding gas flow, are discussed. Analyses of observed surface instabilities and a Fourier decomposition of the flow field reveal asymmetrical azimuthal modulations and broadband instability growth that result in chaotic flow within the wake region.
BibTeX:
@article{MengColonius2018,
  author = {Meng, Jomela C and Colonius, Tim},
  title = {Numerical simulation of the aerobreakup of a water droplet},
  journal = {Journal of Fluid Mechanics},
  year = {2018},
  volume = {835},
  pages = {1108--1135},
  url = {http://colonius.caltech.edu/pdfs/MengColonius2018.pdf},
  doi = {https://doi.org/10.1017/jfm.2017.804}
}
Pishchalnikov, Y., Behnke-Parks, W., Maeda, K., Colonius, T., Mellema, M., Hopcroft, M., Luong, A., Wiener, M., Stoller, M. and Kenny T nd Laser, D. Experimental observations and numerical modeling of lipid-shell microbubbles with stone targeting moieties for minimally-invasive treatment of urinary stones 2018 Proceedings of Meetings on Acoustics
Vol. 35, pp. 020008 
DOI URL 
Abstract: A novel treatment modality incorporating calcium-adhering microbubbles has recently entered human clinical trials as a new minimally-invasive approach to treat urinary stones. In this treatment method, lipid-shell gas-core microbubbles can be introduced into the urinary tract through a catheter. Lipid moities with calcium-adherance properties incorporated into the lipid shell facilitate binding to stones. The microbubbles can be excited by an extracorporeal source of quasi-collimated ultrasound. Alternatively, the microbubbles can be excited by an intraluminal source, such as a fiber-optic laser. With either excitation technique, calcium-adhering microbubbles can significantly increase rates of erosion, pitting, and fragmentation of stones. We report here on new experiments using high-speed photography to characterize microbubble expansion and collapse. The bubble geometry observed in the experiments was used as one of the initial shapes for the numerical modeling. The modeling showed that the bubble dynamics strongly depends on bubble shape and stand-off distance. For the experimentally observed shape of microbubbles, the numerical modeling showed that the collapse of the microbubbles was associated with pressure increases of some two-to-three orders of magnitude compared to the excitation source pressures. This in-vitro study provides key insights into the use of microbubbles with calcium-adhering moieties in treatment of urinary stones.
BibTeX:
@article{PischalnikovBehnkeparksMaedaEtAl2018,
  author = {Pishchalnikov, Y. and Behnke-Parks, W. and Maeda, K. and Colonius, T. and Mellema, M. and Hopcroft, M. and Luong, A. and Wiener, M and Stoller, M and Kenny T nd Laser, D.},
  title = {Experimental observations and numerical modeling of lipid-shell microbubbles with stone targeting moieties for minimally-invasive treatment of urinary stones},
  journal = {Proceedings of Meetings on Acoustics},
  year = {2018},
  volume = {35},
  pages = {020008},
  url = {http://colonius.caltech.edu/pdfs/PishchalnikovBehnkeparksMaedaEtAl2018.pdf},
  doi = {https://doi.org/10.1121/1.5067871}
}
Pishchalnikov, Y., Behnke-Parks, W., Mellema, M., Hopcroft, M., Luong, A., Colonius, T., Maeda, K., Morrison, K. and Laser, D. Urinary stone erosion and fragmentation under low-intensity quasi-collimated ultrasound using gas-filled microbubbles with stone-targeting lipid shells 2018 175th Meeting of the Acoustical Society of America  DOI  
BibTeX:
@inproceedings{PischalnikovBehnkeparksMellemaEtAl2018,
  author = {Pishchalnikov, Y. and Behnke-Parks, W. and Mellema, M. and Hopcroft, M. and Luong, A. and Colonius, T. and Maeda, K. and Morrison, K. and Laser, D.},
  title = {Urinary stone erosion and fragmentation under low-intensity quasi-collimated ultrasound using gas-filled microbubbles with stone-targeting lipid shells},
  booktitle = {175th Meeting of the Acoustical Society of America},
  year = {2018},
  doi = {https://doi.org/10.1121/1.5036106}
}
Schmidt, O.T., Towne, A., Rigas, G., Colonius, T. and Brès, G.A. Spectral analysis of jet turbulence 2018 Journal of Fluid Mechanics
Vol. 855, pp. 953-982 
DOI URL 
Abstract: Informed by large-eddy simulation (LES) data and resolvent analysis of the mean flow, we examine the structure of turbulence in jets in the subsonic, transonic and supersonic regimes. Spectral (frequency-space) proper orthogonal decomposition is used to extract energy spectra and decompose the flow into energy-ranked coherent structures. The educed structures are generally well predicted by the resolvent analysis. Over a range of low frequencies and the first few azimuthal mode numbers, these jets exhibit a low-rank response characterized by Kelvin-Helmholtz (KH) type wavepackets associated with the annular shear layer up to the end of the potential core and that are excited by forcing in the very-near-nozzle shear layer. These modes too have been experimentally observed before and predicted by quasi-parallel stability theory and other approximations - they comprise a considerable portion of the total turbulent energy. At still lower frequencies, particularly for the axisymmetric mode, and again at high frequencies for all azimuthal wavenumbers, the response is not low-rank, but consists of a family of similarly amplified modes. These modes, which are primarily active downstream of the potential core, are associated with the Orr mechanism. They occur also as subdominant modes in the range of frequencies dominated by the KH response. Our global analysis helps tie together previous observations based on local spatial stability theory, and explains why quasi-parallel predictions were successful at some frequencies and azimuthal wavenumbers, but failed at others.
BibTeX:
@article{SchmidtTowneRigasEtAl2018,
  author = {Schmidt, Oliver T and Towne, Aaron and Rigas, Georgios and Colonius, Tim and Brès, Guillaume A},
  title = {Spectral analysis of jet turbulence},
  journal = {Journal of Fluid Mechanics},
  year = {2018},
  volume = {855},
  pages = {953--982},
  url = {http://colonius.caltech.edu/pdfs/SchmidtTowneRigasEtAl2018.pdf},
  doi = {https://doi.org/10.1017/jfm.2018.675}
}
da Silva, A. and Colonius, T. Ensemble-Based State Estimator for Aerodynamic Flows 2018 AIAA Journal
Vol. 56(7) 
DOI URL 
Abstract: Regardless of the plant model, robust flow estimation based on limited measurements remains a major challenge in successful flow control applications. Aiming to combine the robustness of a high-dimensional representation of the dynamics with the cost efficiency of a low-order approximation of the state covariance matrix, a flow state estimator based on the ensemble Kalman filter is applied to two-dimensional flow past a cylinder and an airfoil at high angle of attack and low Reynolds number. For development purposes, the numerical algorithm is used as both the estimator and as a surrogate for the measurements. Estimation is successful using a reduced number of either pressure sensors on the surface of the body or sparsely placed velocity probes in the wake. Because the most relevant features of these flows are restricted to a low-dimensional manifold of the state space, asymptotic behavior of the estimator is shown to be achieved with a small ensemble size. The relative importance of each sensor location is evaluated by analyzing how they influence the estimated flowfield, and optimal locations for pressure sensors are determined. Covariance inflation is used to enhance the estimator performance in the presence of unmodeled freestream perturbations. A combination of parametric modeling and augmented state methodology is used to successfully estimate the forces on immersed bodies subjected to deterministic and random gusts.
BibTeX:
@article{DaSilvaColonius2018,
  author = {da Silva, A.F.C. and Colonius, T.},
  title = {Ensemble-Based State Estimator for Aerodynamic Flows},
  journal = {AIAA Journal},
  year = {2018},
  volume = {56},
  number = {7},
  url = {http://colonius.caltech.edu/pdfs/DaSilvaColonius2018.pdf},
  doi = {https://doi.org/10.2514/1.J056743}
}
da Silva, A.F. and Colonius, T. A Bias-aware EnKF Estimator for Aerodynamic Flows 2018 2018 Fluid Dynamics Conference  DOI URL 
BibTeX:
@inproceedings{DaSilvaColonius2018b,
  author = {da Silva, Andre F. and Colonius, Tim},
  title = {A Bias-aware EnKF Estimator for Aerodynamic Flows},
  booktitle = {2018 Fluid Dynamics Conference},
  publisher = {American Institute of Aeronautics and Astronautics (AIAA)},
  year = {2018},
  url = {http://colonius.caltech.edu/pdfs/DaSilvaColonius2018b.pdf},
  doi = {https://doi.org/10.2514/6.2018-3225}
}
Towne, A., Schmidt, O. and Colonius, T. Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis 2018 Journal of Fluid Mechanics
Vol. 847, pp. 821-867 
DOI URL 
Abstract: We consider the frequency domain form of proper orthogonal decomposition (POD), called spectral proper orthogonal decomposition (SPOD). Spectral POD is derived from a space-time POD problem for statistically stationary flows and leads to modes that each oscillate at a single frequency. This form of POD goes back to the original work of Lumley (Stochastic Tools in Turbulence, Academic Press, 1970), but has been overshadowed by a space-only form of POD since the 1990s. We clarify the relationship between these two forms of POD and show that SPOD modes represent structures that evolve coherently in space and time, while space-only POD modes in general do not. We also establish a relationship between SPOD and dynamic mode decomposition (DMD); we show that SPOD modes are in fact optimally averaged DMD modes obtained from an ensemble DMD problem for stationary flows. Accordingly, SPOD modes represent structures that are dynamic in the same sense as DMD modes but also optimally account for the statistical variability of turbulent flows. Finally, we establish a connection between SPOD and resolvent analysis. The key observation is that the resolvent-mode expansion coefficients must be regarded as statistical quantities to ensure convergent approximations of the flow statistics. When the expansion coefficients are uncorrelated, we show that SPOD and resolvent modes are identical. Our theoretical results and the overall utility of SPOD are demonstrated using two example problems: the complex Ginzburg-Landau equation and a turbulent jet.
BibTeX:
@article{TowneSchmidtColonius2018,
  author = {Towne, A. and Schmidt, O. and Colonius, T.},
  title = {Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis},
  journal = {Journal of Fluid Mechanics},
  year = {2018},
  volume = {847},
  pages = {821--867},
  url = {http://colonius.caltech.edu/pdfs/TowneSchmidtColonius2018.pdf},
  doi = {https://doi.org/10.1017/jfm.2018.283}
}
Veilleux, J.-C., Maeda, K., Colonius, T. and Shepherd, J. Transient Cavitation in Pre-Filled Syringes During Autoinjector Actuation 2018 CAV2018: 10th International Symposium on Cavitation, Baltimore, MD  URL 
BibTeX:
@inproceedings{VeilleuxMaedaColoniusEtAl2018,
  author = {Veilleux, J.-C. and Maeda, K. and Colonius, T. and Shepherd, J.E.},
  title = {Transient Cavitation in Pre-Filled Syringes During Autoinjector Actuation},
  booktitle = {CAV2018: 10th International Symposium on Cavitation, Baltimore, MD},
  year = {2018},
  url = {http://colonius.caltech.edu/pdfs/VeilleuxMaedaColoniusEtAl2018.pdf}
}
An, X., Williams, D.R., da Silva, A.F., Colonius, T. and Eldredge, J. Response of the Separated Flow over an Airfoil to a Short-Time Actuator Burst 2017 47th AIAA Fluid Dynamics Conference  DOI URL 
BibTeX:
@inproceedings{AnWilliamsSilvaEtAl2017,
  author = {An, Xuanhong and Williams, David R. and da Silva, Andre F. and Colonius, Tim and Eldredge, Jeff},
  title = {Response of the Separated Flow over an Airfoil to a Short-Time Actuator Burst},
  booktitle = {47th AIAA Fluid Dynamics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2017},
  url = {http://colonius.caltech.edu/pdfs/AnWilliamsSilvaEtAl2017.pdf},
  doi = {https://doi.org/10.2514/6.2017-3315}
}
Araya, D.B., Colonius, T. and Dabiri, J.O. Transition to bluff-body dynamics in the wake of vertical-axis wind turbines 2017 Journal of Fluid Mechanics
Vol. 813, pp. 346-381 
DOI URL 
Abstract: We present experimental data to demonstrate that the far wake of a vertical-axis wind turbine (VAWT) exhibits features that are quantitatively similar to that of a circular cylinder with the same aspect ratio. For a fixed Reynolds number (Re ≈ 0.8 × 10^5) and variable tip-speed ratio, two-dimensional particle image velocimetry (PIV) is used to measure the velocity field in the wake of four different laboratory-scale models: a 2-bladed, 3-bladed and 5-bladed VAWT, as well as a circular cylinder. With these measurements, we use spectral analysis and proper orthogonal decomposition (POD) to evaluate statistics of the velocity field and investigate the large-scale coherent motions of the wake. In all cases, we observe three distinct regions in the VAWT wake: (i) the near wake, where periodic blade vortex shedding dominates; (ii) a transition region, where growth of a shear-layer instability occurs; (iii) the far wake, where bluff-body wake oscillations dominate. We define a dynamic solidity parameter, _D, that relates the characteristic scales of the flow to the streamwise transition location in the wake. In general, we find that increasing  _D leads to an earlier transition, a greater initial velocity deficit and a faster rate of recovery in the wake. We propose a coordinate transformation using  _D in which the minimum velocity recovery profiles of the VAWT wake closely match that of the cylinder wake. The results have implications for manipulating VAWT wake recovery within a wind farm.
BibTeX:
@article{ArayaColoniusDabiri2017,
  author = {Araya, Daniel B. and Colonius, Tim and Dabiri, John O.},
  title = {Transition to bluff-body dynamics in the wake of vertical-axis wind turbines},
  journal = {Journal of Fluid Mechanics},
  year = {2017},
  volume = {813},
  pages = {346--381},
  url = {http://colonius.caltech.edu/pdfs/ArayaColoniusDabiri2017.pdf},
  doi = {https://doi.org/10.1017/jfm.2016.862}
}
Bailey, M., Simon, J.C., Kreider, W., Dunmire, B., Crum, L., Maxwell, A.D., Khokhlova, V., Sapozhnikov, O.A., Cleveland, R., Colonius, T. and others Innovative strategies for improved outcomes in nephrolithiasis 2017 3rd Joint Meeting Of The Acoustical Society Of America And The European Acoustics Association  DOI  
BibTeX:
@inproceedings{BaileySimonKreiderEtAl2017,
  author = {Bailey, Michael and Simon, Julianna C and Kreider, Wayne and Dunmire, Barbrina and Crum, Lawrence and Maxwell, Adam D and Khokhlova, Vera and Sapozhnikov, Oleg A and Cleveland, Robin and Colonius, Tim and others},
  title = {Innovative strategies for improved outcomes in nephrolithiasis},
  booktitle = {3rd Joint Meeting Of The Acoustical Society Of America And The European Acoustics Association},
  year = {2017},
  doi = {https://doi.org/10.1121/1.4988643}
}
Breakey, D.E., Jordan, P., Cavalieri, A.V., Nogueira, P.A., Léon, O., Colonius, T. and Rodr\iguez, D. Experimental study of turbulent-jet wave packets and their acoustic efficiency 2017 Physical Review Fluids
Vol. 2(12), pp. 124601 
DOI URL 
Abstract: This paper details the statistical and time-resolved analysis of the relationship between the near-field pressure fluctuations of unforced, subsonic free jets (0.4 le M le 0.6) and their far-field sound emissions. Near-field and far-field microphone measurements were taken on a conical array close to the jets and an azimuthal ring at 20◦ to the jet axis, respectively. Recent velocity and pressure measurements indicate the presence of linear wave packets in the near field by closely matching predictions from the linear homogenous parabolized stability equations, but the agreement breaks down both beyond the end of the potential core and when considering higher order statistical moments, such as the two-point coherence. Proper orthogonal decomposition (POD), interpreted in terms of inhomogeneous linear models using the resolvent framework allows us to understand these discrepancies. A new technique is developed for projecting time-domain pressure measurements onto a statistically obtained POD basis, yielding the time-resolved activity of each POD mode and its correlation with the far field. A single POD mode, interpreted as an optimal high-gain structure that arises due to turbulent forcing, captures the salient near-field–far-field correlation signature; further, the signatures of the next two modes, understood as suboptimally forced structures, suggest that these POD modes represent higher order, acoustically important near-field behavior. An existing Green’s-function-based technique is used to make far-field predictions, and results are interpreted in terms of POD/resolvent modes, indicating the acoustic importance of this higher order behavior. The technique is extended to provide time-domain far-field predictions.
BibTeX:
@article{BreakeyJordanCavalieriEtAl2017,
  author = {Breakey, David ES and Jordan, Peter and Cavalieri, André VG and Nogueira, Petrônio A and Léon, Olivier and Colonius, Tim and Rodr\iguez, Daniel},
  title = {Experimental study of turbulent-jet wave packets and their acoustic efficiency},
  journal = {Physical Review Fluids},
  year = {2017},
  volume = {2},
  number = {12},
  pages = {124601},
  url = {http://colonius.caltech.edu/pdfs/BreakeyJordanCavalieriEtAl2017.pdf},
  doi = {https://doi.org/10.1103/physrevfluids.2.124601}
}
de Castro da Silva, A.F. and Colonius, T. An EnKF-based Flow State Estimator for Aerodynamic Flows 2017 8th AIAA Theoretical Fluid Mechanics Conference  DOI URL 
BibTeX:
@inproceedings{SilvaColonius2017,
  author = {de Castro da Silva, Andre Fernando and Colonius, Tim},
  title = {An EnKF-based Flow State Estimator for Aerodynamic Flows},
  booktitle = {8th AIAA Theoretical Fluid Mechanics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2017},
  url = {http://colonius.caltech.edu/pdfs/SilvaColonius2017.pdf},
  doi = {https://doi.org/10.2514/6.2017-3483}
}
Goza, A. and Colonius, T. A global mode analysis of flapping flags 2017 TSFP DIGITAL LIBRARY ONLINE  URL 
BibTeX:
@inproceedings{GozaColonius2017b,
  author = {Goza, Andres and Colonius, Timothy},
  title = {A global mode analysis of flapping flags},
  booktitle = {TSFP DIGITAL LIBRARY ONLINE},
  publisher = {Begel House Inc.},
  year = {2017},
  url = {http://www.tsfp-conference.org/proceedings/2017/2/333.pdf}
}
Goza, A. and Colonius, T. A strongly-coupled immersed-boundary formulation for thin elastic structures 2017 Journal of Computational Physics
Vol. 336, pp. 401-411 
DOI URL 
Abstract: We present a strongly-coupled immersed-boundary method for flow–structure interaction problems involving thin deforming bodies. The method is stable for arbitrary choices of solid-to-fluid mass ratios and for large body motions. As with many strongly-coupled
immersed-boundary methods, our method requires the solution of a nonlinear algebraic system at each time step. The system is solved through iteration, where the iterates are obtained by linearizing the system and performing a block-LU factorization. This restricts all iterations to small-dimensional subsystems that scale with the number of discretization points on the immersed surface, rather than on the entire flow domain. Moreover, the iteration procedure we propose does not involve heuristic regularization parameters, and has converged in a small number of iterations for all problems we have considered. We derive our method for general deforming surfaces, and verify the method with two-dimensional test problems of geometrically nonlinear flags undergoing large amplitude flapping behavior.
BibTeX:
@article{GozaColonius2017,
  author = {Andres Goza and Tim Colonius},
  title = {A strongly-coupled immersed-boundary formulation for thin elastic structures},
  journal = {Journal of Computational Physics},
  year = {2017},
  volume = {336},
  pages = {401--411},
  url = {http://colonius.caltech.edu/pdfs/GozaColonius2017.pdf},
  doi = {https://doi.org/10.1016/j.jcp.2017.02.027}
}
Kleine, V.G., Sasaki, K., Cavalieri, A., Brès, G.A. and Colonius, T. Evaluation of PSE as a Model for Supersonic Jet Using Transfer Functions 2017 23rd AIAA/CEAS Aeroacoustics Conference  DOI URL 
BibTeX:
@inproceedings{KleineSasakiCavalieriEtAl2017,
  author = {Kleine, Vitor G. and Sasaki, Kenzo and Cavalieri, AndréV. and Brès, Guillaume A. and Colonius, Tim},
  title = {Evaluation of PSE as a Model for Supersonic Jet Using Transfer Functions},
  booktitle = {23rd AIAA/CEAS Aeroacoustics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2017},
  url = {http://colonius.caltech.edu/pdfs/KleineSasakiCavalieriEtAl2017.pdf},
  doi = {https://doi.org/10.2514/6.2017-4194}
}
Liska, S. and Colonius, T. A fast immersed boundary method for external incompressible viscous flows using lattice Green's functions 2017 Journal of Computational Physics
Vol. 331, pp. 257-279 
DOI URL 
Abstract: A new parallel, computationally efficient immersed boundary method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. Immersed surfaces with prescribed motions' are generated using the interpolation and regularization operators obtained from the discrete delta function approach of the original (Peskin's) immersed boundary method. Unlike Peskin's method, boundary forces are regarded as Lagrange multipliers that are used to satisfy the no-slip condition. The incompressible Navier-Stokes equations are discretized on an unbounded staggered Cartesian grid and are solved in a finite number of operations using lattice Green's function techniques. These techniques are used to automatically enforce the natural free-space boundary conditions and to implement a novel block-wise adaptive grid that significantly reduces the run-time cost of solutions by limiting operations to grid cells in the immediate vicinity and near-wake region of the immersed surface. These techniques also enable the construction of practical discrete viscous integrating factors that are used in combination with specialized half-explicit Runge-Kutta schemes to accurately and efficiently solve the differential algebraic equations describing the discrete momentum equation, incompressibility constraint, and no-slip constraint. Linear systems of equations resulting from the time integration scheme are efficiently solved using an approximation-free nested projection technique. The algebraic properties of the discrete operators are used to reduce projection steps to simple discrete elliptic problems, e.g. discrete Poisson problems, that are compatible with recent parallel fast multipole methods for difference equations. Numerical experiments on low-aspect-ratio flat plates and spheres at Reynolds numbers up to 3700 are used to verify the accuracy and physical fidelity of the formulation.
BibTeX:
@article{LiskaColonius2017,
  author = {Liska, S. and Colonius, T.},
  title = {A fast immersed boundary method for external incompressible viscous flows using lattice Green's functions},
  journal = {Journal of Computational Physics},
  year = {2017},
  volume = {331},
  pages = {257--279},
  url = {http://colonius.caltech.edu/pdfs/LiskaColonius2017.pdf},
  doi = {https://doi.org/10.1016/j.jcp.2016.11.034}
}
Maeda, K. and Colonius, T. A source term approach for generation of one-way acoustic waves in the Euler and Navier--Stokes equations 2017 Wave Motion
Vol. 75, pp. 36-49 
DOI URL 
Abstract: We derive a volumetric source term for the Euler and Navier-Stokes equations that mimics the generation of unidirectional acoustic waves from an arbitrary smooth surface in three-dimensional space. The model is constructed as a linear combination of monopole and dipole sources in the mass, momentum, and energy equations. The singular source distribution on the surface is regularized on a computational grid by convolution with a smeared Dirac delta function. The source is implemented in the Euler equation using a Cartesian-grid finite-volume WENO scheme, and validated by comparing with analytical solution for unidirectional planar and spherical acoustic waves. Using the scheme, we emulate a spherical piezoelectric transducer and a multi-element array medical transducer to simulate focused ultrasound fields in water. The simulated ultrasound fields show favorable agreement with previous experiments.
BibTeX:
@article{MaedaColonius2017,
  author = {Maeda, Kazuki and Colonius, Tim},
  title = {A source term approach for generation of one-way acoustic waves in the Euler and Navier--Stokes equations},
  journal = {Wave Motion},
  year = {2017},
  volume = {75},
  pages = {36--49},
  url = {http://colonius.caltech.edu/pdfs/MaedaColonius2017.pdf},
  doi = {https://doi.org/10.1016/j.wavemoti.2017.08.004}
}
Maeda, K., Colonius, T., Kreider, W., Maxwell, A.D. and Bailey, M. Quantification of the shielding of kidney stones by bubble clouds during burst wave lithotripsy 2017 3rd Joint Meeting Of The Acoustical Society Of America And The European Acoustics Association  DOI  
BibTeX:
@inproceedings{MaedaColoniusKreiderEtAl2017,
  author = {Maeda, Kazuki and Colonius, Tim and Kreider, Wayne and Maxwell, Adam D and Bailey, Michael},
  title = {Quantification of the shielding of kidney stones by bubble clouds during burst wave lithotripsy},
  booktitle = {3rd Joint Meeting Of The Acoustical Society Of America And The European Acoustics Association},
  year = {2017},
  doi = {https://doi.org/10.1121/1.4987968}
}
McAteer, J., Evan, A.P., Lingeman, J.E., Willis, L.R., Blomgren, P.M., Williams, J.C., Handa, R., Connors, B.A., Crum, L., Bailey, M. and others Ed Carstensen, advisor and mentor to the shockwave lithotripsy program project group 2017 3rd Joint Meeting Of The Acoustical Society Of America And The European Acoustics Association  DOI  
BibTeX:
@inproceedings{McAteerEvanLingemanEtAl2017,
  author = {McAteer, James and Evan, Andrew P and Lingeman, James E and Willis, Lynn R and Blomgren, Philip M and Williams, James C and Handa, Rajash and Connors, Bret A and Crum, Lawrence and Bailey, Michael and others},
  title = {Ed Carstensen, advisor and mentor to the shockwave lithotripsy program project group},
  booktitle = {3rd Joint Meeting Of The Acoustical Society Of America And The European Acoustics Association},
  year = {2017},
  doi = {https://doi.org/10.1121/1.4988642}
}
Mengaldo, G., Liska, S., Yu, K., Colonius, T. and Jardin, T. Immersed Boundary Lattice Green's Function methods for External Aerodynamics 2017 23rd AIAA Computational Fluid Dynamics Conference  DOI URL 
BibTeX:
@inproceedings{MengaldoLiskaYuEtAl2017,
  author = {Mengaldo, Gianmarco and Liska, Sebastian and Yu, Ke and Colonius, Tim and Jardin, Thierry},
  title = {Immersed Boundary Lattice Green's Function methods for External Aerodynamics},
  booktitle = {23rd AIAA Computational Fluid Dynamics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2017},
  url = {http://colonius.caltech.edu/pdfs/MengaldoLiskaYuEtAl2017.pdf},
  doi = {https://doi.org/10.2514/6.2017-3621}
}
Rigas, G., Colonius, T. and Beyar, M. Stability of wall-bounded flows using one-way spatial integration of Navier-Stokes equations 2017 55th AIAA Aerospace Sciences Meeting  DOI URL 
BibTeX:
@inproceedings{RigasColoniusBeyar2017,
  author = {Georgios Rigas and Tim Colonius and Michael Beyar},
  title = {Stability of wall-bounded flows using one-way spatial integration of Navier-Stokes equations},
  booktitle = {55th AIAA Aerospace Sciences Meeting},
  year = {2017},
  url = {http://colonius.caltech.edu/pdfs/RigasColoniusBeyar2017.pdf},
  doi = {https://doi.org/10.2514/6.2017-1881}
}
Rigas, G., Schmidt, O.T., Colonius, T. and Brès, G.A. One Way Navier-Stokes and resolvent analysis for modeling coherent structures in a supersonic turbulent jet 2017 23rd AIAA/CEAS Aeroacoustics Conference  DOI URL 
BibTeX:
@inproceedings{RigasSchmidtColoniusEtAl2017,
  author = {Rigas, Georgios and Schmidt, Oliver T. and Colonius, Tim and Brès, Guillaume A.},
  title = {One Way Navier-Stokes and resolvent analysis for modeling coherent structures in a supersonic turbulent jet},
  booktitle = {23rd AIAA/CEAS Aeroacoustics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2017},
  url = {http://colonius.caltech.edu/pdfs/RigasSchmidtColoniusEtAl2017.pdf},
  doi = {https://doi.org/10.2514/6.2017-4046}
}
Sasaki, K., Cavalieri, A.V., Jordan, P., Schmidt, O.T., Colonius, T. and Brès, G.A. High-frequency wavepackets in turbulent jets 2017 Journal of Fluid Mechanics
Vol. 830, pp. R2 
DOI URL 
Abstract: Wavepackets obtained as solutions of the flow equations linearised around the mean flow have been shown in recent work to yield good agreement, in terms of amplitude and phase, with those educed from turbulent jets. Compelling agreement has been demonstrated, for the axisymmetric and first helical mode, up to Strouhal numbers close to unity. We here extend the range of validity of wavepacket models to Strouhal number St = 4.0 and azimuthal wavenumber m = 4 by comparing solutions of the parabolised stability equations with a well-validated large-eddy simulation of a Mach 0.9 turbulent jet. The results show that the near-nozzle dynamics can be correctly described by the homogeneous linear model, the initial growth rates being accurately predicted for the entire range of frequencies and azimuthal wavenumbers considered. Similarly to the lower-frequency wavepackets reported prior to this work, the high-frequency linear waves deviate from the data downstream of their stabilisation locations, which move progressively upstream as the frequency increases.
BibTeX:
@article{SasakiCavalieriJordanEtAl2017,
  author = {Sasaki, Kenzo and Cavalieri, André VG and Jordan, Peter and Schmidt, Oliver T and Colonius, Tim and Brès, Guillaume A},
  title = {High-frequency wavepackets in turbulent jets},
  journal = {Journal of Fluid Mechanics},
  year = {2017},
  volume = {830},
  pages = {R2},
  url = {http://colonius.caltech.edu/pdfs/SasakiCavalieriJordanEtAl2017.pdf},
  doi = {https://doi.org/10.1017/jfm.2017.659}
}
Schmidt, O., Colonius, T. and Brès, G.A. Wavepacket intermittency and its role in turbulent jet noise 2017 55th AIAA Aerospace Sciences Meeting  DOI URL 
BibTeX:
@inproceedings{SchmidtColoniusBres2017,
  author = {Oliver Schmidt and Tim Colonius and Guillaume A. Brès},
  title = {Wavepacket intermittency and its role in turbulent jet noise},
  booktitle = {55th AIAA Aerospace Sciences Meeting},
  year = {2017},
  url = {http://colonius.caltech.edu/pdfs/SchmidtColoniusBres2017.pdf},
  doi = {https://doi.org/10.2514/6.2017-0686}
}
Schmidt, O.T., Towne, A., Colonius, T., Cavalieri, A.V., Jordan, P. and Brès, G.A. Wavepackets and trapped acoustic modes in a turbulent jet: coherent structure eduction and global stability 2017 Journal of Fluid Mechanics
Vol. 825, pp. 1153-1181 
DOI URL 
Abstract: Coherent features of a turbulent Mach 0.9, Reynolds number 10(6) jet are educed from a high-fidelity large eddy simulation. Besides the well-known Kelvin-Helmholtz instabilities of the shear layer, a new class of trapped acoustic waves is identified in the potential core. A global linear stability analysis based on the turbulent mean flow is conducted. The trapped acoustic waves form branches of discrete eigenvalues in the global spectrum, and the corresponding global modes accurately match the educed structures. Discrete trapped acoustic modes occur in a hierarchy determined by their radial and axial order. A local dispersion relation is constructed from the global modes and found to agree favourably with an empirical dispersion relation educed from the simulation data. The product between direct and adjoint modes is then used to isolate the trapped waves. Under certain conditions, resonance in the form of a beating occurs between trapped acoustic waves of positive and negative group velocities. This resonance explains why the trapped modes are prominently observed in the simulation and as tones in previous experimental studies. In the past, these tones were attributed to external factors. Here, we show that they are an intrinsic feature of high-subsonic jets that can be unambiguously identified by a global linear stability analysis.
BibTeX:
@article{SchmidtTowneColoniusEtAl2017,
  author = {Schmidt, Oliver T and Towne, Aaron and Colonius, Tim and Cavalieri, André VG and Jordan, Peter and Brès, Guillaume A},
  title = {Wavepackets and trapped acoustic modes in a turbulent jet: coherent structure eduction and global stability},
  journal = {Journal of Fluid Mechanics},
  year = {2017},
  volume = {825},
  pages = {1153--1181},
  url = {http://colonius.caltech.edu/pdfs/SchmidtTowneColoniusEtAl2017.pdf},
  doi = {https://doi.org/10.1017/jfm.2017.407}
}
Sharma, A., Theofilis, V. and Colonius, T. Special issue on global flow instability and control 2017 Theoretical and Computational Fluid Dynamics
Vol. 31, pp. 471-474 
DOI URL 
Abstract: This special issue is the second on the topic of "Global Flow Instability and Control," following the first in 2011. As with the previous special issue, the participants of the last two symposia on Global Flow Instability and Control, held in Crete, Greece, were invited to submit publications. These papers were peer reviewed according to the standards of the journal, and this issue represents a snapshot of the progress since 2011. In this preface, a sampling of important developments in the field since the first issue is discussed. A synopsis of the papers in this issue is given in that context.
BibTeX:
@article{SharmaTheofilisColonius2017,
  author = {Sharma, Ati and Theofilis, Vassilis and Colonius, Tim},
  title = {Special issue on global flow instability and control},
  journal = {Theoretical and Computational Fluid Dynamics},
  year = {2017},
  volume = {31},
  pages = {471--474},
  url = {http://colonius.caltech.edu/pdfs/SharmaTheofilisColonius2017.pdf},
  doi = {https://doi.org/10.1007/s00162-017-0444-y}
}
Sinha, A., Towne, A., Colonius, T., Schlinker, R.H., Reba, R., Simonich, J.C. and Shannon, D.W. Active Control of Noise from Hot Supersonic Jets 2017 AIAA Journal
Vol. 56(3), pp. 933-948 
DOI URL 
Abstract: This paper presents diagnostic experiments aimed at understanding and mitigating supersonic jet noise from the coherent wave-packet structures that are the source of peak aft-angle mixing noise. Both isothermal and heated, nearly perfectly expanded, Mach 1.5 jets were forced in the near-nozzle region with air injection generated by a spinning-valve device designed to excite the jet at frequencies approaching those of the dominant turbulent structures. Substantial reductions in the peak aft-angle radiation were achieved with steady blowing at amplitudes corresponding to 2-6% of the mass flow rate of the primary jet. The noise benefit saturated at mass flow rates above 4%, with as much as a 6 dB reduction in overall sound pressure level at aft angles. Increasing the mass flow rates yielded a monotonically increasing high-frequency noise penalty at the sideline, where noise levels in the natural jet were already 15 dB lower than the aft-angle peak, so that the penalty due to actuation was minor. Although both steady and periodic unsteady mass injections were produced by the spinning valve when it rotated, it was calibrated to hold the steady mass flow rate constant as the frequency of unsteady blowing was changed. In this way, the effect of steady and unsteady blowings on the acoustic field could be decoupled. It is shown that the noise benefit was uniquely associated with the steady component of blowing, whereas the unsteady component resulted in additive tones in the spectra. This implied linearity is consistent with theory and experiments showing that the wave-packet structures, which give rise to the dominant aft-angle radiation, evolve in the turbulent mean flowfield in a nearly linear fashion from their origin in the near-nozzle region. The interpretation of noise reduction is that the steady component of blowing spreads the mean flow more rapidly, resulting in weaker wave packets. Periodic unsteady blowing forces coherent wave packets that are largely uncorrelated from the random natural ones, which then leads to the observed additive tones.
BibTeX:
@article{SinhaTowneColoniusEtAl2017,
  author = {Sinha, Aniruddha and Towne, Aaron and Colonius, Tim and Schlinker, Robert H and Reba, Ramons and Simonich, John C and Shannon, Daniel W},
  title = {Active Control of Noise from Hot Supersonic Jets},
  journal = {AIAA Journal},
  year = {2017},
  volume = {56},
  number = {3},
  pages = {933--948},
  url = {http://colonius.caltech.edu/pdfs/SinhaTowneColoniusEtAl2017.pdf},
  doi = {https://doi.org/10.2514/1.J056159}
}
Taira, K., Brunton, S.L., Dawson, S., Rowley, C.W., Colonius, T., McKeon, B.J., Schmidt, O.T., Gordeyev, S., Theofilis, V. and Ukeiley, L.S. Modal analysis of fluid flows: An overview 2017 AIAA Journal
Vol. 55(12), pp. 4013-4031 
DOI URL 
BibTeX:
@article{TairaBruntonDawsonEtAl2017,
  author = {Taira, Kunihiko and Brunton, Steven L and Dawson, Scott and Rowley, Clarence W and Colonius, Tim and McKeon, Beverley J and Schmidt, Oliver T and Gordeyev, Stanislav and Theofilis, Vassilios and Ukeiley, Lawrence S},
  title = {Modal analysis of fluid flows: An overview},
  journal = {AIAA Journal},
  year = {2017},
  volume = {55},
  number = {12},
  pages = {4013--4031},
  url = {http://colonius.caltech.edu/pdfs/TairaBruntonDawsonEtAl2017.pdf},
  doi = {https://doi.org/10.2514/1.j056060}
}
Towne, A., Cavalieri, A.V., Jordan, P., Colonius, T., Schmidt, O., Jaunet, V. and Brès, G.A. Acoustic resonance in the potential core of subsonic jets 2017 Journal of Fluid Mechanics
Vol. 825, pp. 1113-1152 
DOI URL 
Abstract: The purpose of this paper is to characterize and model waves that are observed within the potential core of subsonic jets and relate them to previously observed tones in the near-nozzle region. The waves are detected in data from a large-eddy simulation of a Mach 0.9 isothermal jet and modelled using parallel and weakly non-parallel linear modal analysis of the Euler equations linearized about the turbulent mean flow, as well as simplified models based on a cylindrical vortex sheet and the acoustic modes of a cylindrical soft duct. In addition to the Kelvin–Helmholtz instability waves, three types of waves with negative phase velocities are identified in the potential core: upstream- and downstream-propagating duct-like acoustic modes that experience the shear layer as a pressure-release surface and are therefore radially confined to the potential core, and upstream-propagating acoustic modes that represent a weak coupling between the jet core and the free stream. The slow streamwise contraction of the potential core imposes a frequency-dependent end condition on the waves that is modelled as the turning points of a weakly non-parallel approximation of the waves. These turning points provide a mechanism by which the upstream- and downstream-travelling waves can interact and exchange energy through reflection and transmission processes. Paired with a second end condition provided by the nozzle, this leads to the possibility of resonance in limited frequency bands that are bound by two saddle points in the complex wavenumber plane. The predicted frequencies closely match the observed tones detected outside of the jet. The vortex-sheet model is then used to systematically explore the Mach number and temperature ratio dependence of the phenomenon. For isothermal jets, the model suggests that resonance is likely to occur in a narrow range of Mach number, 0.82 < M < 1.
BibTeX:
@article{TowneCavalieriJordanEtAl2017,
  author = {Towne, Aaron and Cavalieri, André VG and Jordan, Peter and Colonius, Tim and Schmidt, Oliver and Jaunet, Vincent and Brès, Guillaume A},
  title = {Acoustic resonance in the potential core of subsonic jets},
  journal = {Journal of Fluid Mechanics},
  year = {2017},
  volume = {825},
  pages = {1113--1152},
  url = {http://colonius.caltech.edu/pdfs/TowneCavalieriJordanEtAl2017.pdf},
  doi = {https://doi.org/10.1017/jfm.2017.346}
}
An, X., Williams, D.R., Eldredge, J. and Colonius, T. Modeling Dynamic Lift Response to Actuation 2016 54th AIAA Aerospace Sciences Meeting  DOI URL 
BibTeX:
@inproceedings{AnWilliamsEldredgeEtAl2016,
  author = {Xuanhong An and David R. Williams and Jeff Eldredge and Tim Colonius},
  title = {Modeling Dynamic Lift Response to Actuation},
  booktitle = {54th AIAA Aerospace Sciences Meeting},
  publisher = {American Institute of Aeronautics and Astronautics (AIAA)},
  year = {2016},
  url = {http://colonius.caltech.edu/pdfs/AnWilliamsEldredgeEtAl2016.pdf},
  doi = {https://doi.org/10.2514/6.2016-0058}
}
Brès, G.A., Jaunet, V., Rallic, M.L., Jordan, P., Towne, A., Schmidt, O., Colonius, T., Cavalieri, A.V. and Lele, S.K. Large eddy simulation for jet noise: azimuthal decomposition and intermittency of the radiated sound 2016 22nd AIAA/CEAS Aeroacoustics Conference  DOI URL 
BibTeX:
@inproceedings{BresJaunetRallicEtAl2016,
  author = {Guillaume A. Brès and Vincent Jaunet and Maxime Le Rallic and Peter Jordan and Aaron Towne and Oliver Schmidt and Tim Colonius and André V. Cavalieri and Sanjiva K. Lele},
  title = {Large eddy simulation for jet noise: azimuthal decomposition and intermittency of the radiated sound},
  booktitle = {22nd AIAA/CEAS Aeroacoustics Conference},
  publisher = {American Institute of Aeronautics and Astronautics (AIAA)},
  year = {2016},
  url = {http://colonius.caltech.edu/pdfs/BresJaunetRallicEtAl2016.pdf},
  doi = {https://doi.org/10.2514/6.2016-3050}
}
Cavalieri, A.V., Sasaki, K., Jordan, P., Schmidt, O., Colonius, T. and Brès, G.A. High-frequency wavepackets in turbulent jets 2016 22nd AIAA/CEAS Aeroacoustics Conference  DOI URL 
BibTeX:
@inproceedings{CavalieriSasakiJordanEtAl2016,
  author = {André V. Cavalieri and Kenzo Sasaki and Peter Jordan and Oliver Schmidt and Tim Colonius and Guillaume A. Brès},
  title = {High-frequency wavepackets in turbulent jets},
  booktitle = {22nd AIAA/CEAS Aeroacoustics Conference},
  publisher = {American Institute of Aeronautics and Astronautics (AIAA)},
  year = {2016},
  url = {http://colonius.caltech.edu/pdfs/CavalieriSasakiJordanEtAl2016.pdf},
  doi = {https://doi.org/10.2514/6.2016-3056}
}
Choi, J. Unsteady aerodynamics and optimal control of an airfoil at low Reynolds number 2016 School: California Institute of Technology  URL 
Abstract: As opposed to conventional air vehicles that have fixed wings, small birds and insects are known to flap their wings at higher angles of attack. The vortex produced at the tip of the wing, known as the leading-edge vortex (LEV), plays an important role to enhance lift during its flight. In this thesis, we analyze the influence of these vortices on aerodynamic forces that could be beneficial to micro-air vehicle performance and efficiency. The flow structures associated with simple harmonic motions of an airfoil are first investigated. The characteristics of the time-averaged and fluctuating forces are explained by analyzing vortical flow features, such as vortex lock-in, leading-edge vortex synchronization, and vortex formation time. Specific frequency regions where the wake instability locks in to the unsteady motion of the airfoil are identified, and these lead to significant changes in the mean forces. A detailed study of the flow structures associated with the LEV acting either in- or out-of-phase with the quasi-steady component of the forces is performed to quantify the amplification and attenuation behavior of the fluctuating forces. An inherent time scale of the LEV associated with its formation and detachment (LEV formation time) is shown to control the time-averaged forces. With these results, several optimal flow control problems are formulated. Adjoint-based optimal control is applied to an airfoil moving at a constant velocity and also to a reciprocating airfoil with no forward velocity. In both cases, we maximize lift by controlling the pitch rate of the airfoil. For the former case, the static map of lift at various angles of attack is additionally examined to find the static angle that provides maximum lift and also to confirm whether the optimizations perform according to the static map. For the latter case, we obtain a solution of the optimized motion of the flapping airfoil which resembles that of a hovering insect.
BibTeX:
@phdthesis{Choi2016,
  author = {Jeesoon Choi},
  title = {Unsteady aerodynamics and optimal control of an airfoil at low Reynolds number},
  school = {California Institute of Technology},
  year = {2016},
  url = {http://resolver.caltech.edu/CaltechTHESIS:05272016-220450949}
}
Colonius, T., Towne, A. and Schmidt, O. Models of Coherent Structures in Turbulent Jets and their Radiated Sound 2016 XXXIV ICTAM, Montreal, Canada  URL 
BibTeX:
@inproceedings{ColoniusTowneSchmidt2016,
  author = {Tim Colonius and Aaron Towne and Oliver Schmidt},
  title = {Models of Coherent Structures in Turbulent Jets and their Radiated Sound},
  booktitle = {XXXIV ICTAM, Montreal, Canada},
  year = {2016},
  url = {http://colonius.caltech.edu/pdfs/ColoniusTowneSchmidt2016.pdf}
}
Darakananda, D., Eldredge, J., Colonius, T. and Williams, D.R. A Vortex Sheet/Point Vortex Dynamical Model For Unsteady Separated Flows 2016 54th AIAA Aerospace Sciences Meeting  DOI URL 
BibTeX:
@inproceedings{DarakanandaEldredgeColoniusEtAl2016,
  author = {Darwin Darakananda and Jeff Eldredge and Tim Colonius and David R. Williams},
  title = {A Vortex Sheet/Point Vortex Dynamical Model For Unsteady Separated Flows},
  booktitle = {54th AIAA Aerospace Sciences Meeting},
  publisher = {American Institute of Aeronautics and Astronautics (AIAA)},
  year = {2016},
  url = {http://colonius.caltech.edu/pdfs/DarakanandaEldredgeColoniusEtAl2016.pdf},
  doi = {https://doi.org/10.2514/6.2016-2072}
}
Goza, A., Liska, S., Morley, B. and Colonius, T. Accurate computation of surface stresses and forces with immersed boundary methods 2016 Journal of Computational Physics
Vol. 321, pp. 860-873 
DOI URL 
Abstract: Many immersed boundary methods solve for surface stresses that impose the velocity boundary conditions on an immersed body. These surface stresses may contain spurious oscillations that make them ill-suited for representing the physical surface stresses on the body. Moreover, these inaccurate stresses often lead to unphysical oscillations in the history of integrated surface forces such as the coefficient of lift. While the errors in the surface stresses and forces do not necessarily affect the convergence of the velocity field, it is desirable, especially in fluid–structure interaction problems, to obtain smooth and convergent stress distributions on the surface. To this end, we show that the equation for the surface stresses is an integral equation of the first kind whose ill-posedness is the source of spurious oscillations in the stresses. We also demonstrate that for sufficiently smooth delta functions, the oscillations may be filtered out to obtain physically accurate surface stresses. The filtering is applied as a post-processing procedure, so that the convergence of the velocity field is unaffected. We demonstrate the efficacy of the method by computing stresses and forces that converge to the physical stresses and forces for several test problems.
BibTeX:
@article{GozaLiskaMorleyEtAl2016,
  author = {Andres Goza and Sebastian Liska and Benjamin Morley and Tim Colonius},
  title = {Accurate computation of surface stresses and forces with immersed boundary methods},
  journal = {Journal of Computational Physics},
  year = {2016},
  volume = {321},
  pages = {860-873},
  url = {http://colonius.caltech.edu/pdfs/GozaLiskaMorleyEtAl2016.pdf},
  doi = {https://doi.org/10.1016/j.jcp.2016.06.014}
}
Jaunet, V., Jordan, P., Cavalieri, A.V., Towne, A., Colonius, T., Schmidt, O. and Brès, G.A. Tonal dynamics and sound in subsonic turbulent jets 2016 22nd AIAA/CEAS Aeroacoustics Conference  DOI URL 
BibTeX:
@inproceedings{JaunetJordanCavalieriEtAl2016,
  author = {Vincent Jaunet and Peter Jordan and André V. Cavalieri and Aaron Towne and Tim Colonius and Oliver Schmidt and Guillaume A. Brès},
  title = {Tonal dynamics and sound in subsonic turbulent jets},
  booktitle = {22nd AIAA/CEAS Aeroacoustics Conference},
  publisher = {American Institute of Aeronautics and Astronautics (AIAA)},
  year = {2016},
  url = {http://colonius.caltech.edu/pdfs/JaunetJordanCavalieriEtAl2016.pdf},
  doi = {https://doi.org/10.2514/6.2016-3016}
}
Lee, H.J., Sherrit, S., Tosi, L.P. and Colonius, T. Design and experimental evaluation of flextensional-cantilever based piezoelectric transducers for flow energy harvesting 2016 SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring  DOI URL 
BibTeX:
@inproceedings{LeeSherritTosiEtAl2016,
  author = {Lee, H. J. and Sherrit, S. and Tosi, L. P. and Colonius, T.},
  title = {Design and experimental evaluation of flextensional-cantilever based piezoelectric transducers for flow energy harvesting},
  booktitle = {SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring},
  year = {2016},
  url = {http://colonius.caltech.edu/pdfs/LeeSherritTosiEtAl2016.pdf},
  doi = {https://doi.org/10.1117/12.2219269}
}
Liska, S. Fast Lattice Green's Function Methods for Viscous Incompressible Flows on Unbounded Domains 2016 School: California Institute of Technology  URL 
Abstract: In this thesis, a collection of novel numerical techniques culminating in a fast, parallel method for the direct numerical simulation of incompressible viscous flows around surfaces immersed in unbounded fluid domains is presented. At the core of all these techniques is the use of the fundamental solutions, or lattice Green?s functions, of discrete operators to solve inhomogeneous elliptic difference equations arising in the discretization of the three-dimensional incompressible Navier-Stokes equations on unbounded regular grids. In addition to automatically enforcing the natural free-space boundary conditions, these new lattice Green?s function techniques facilitate the implementation of robust staggered-Cartesian-grid flow solvers with efficient nodal distributions and fast multipole methods. The provable conservation and stability properties of the appropriately combined discretization and solution techniques ensure robust numerical solutions. Numerical experiments on thin vortex rings, low-aspect-ratio flat plates, and spheres are used verify the accuracy, physical fidelity, and computational efficiency of the present formulations.
BibTeX:
@phdthesis{Liska2016,
  author = {Sebastian Liska},
  title = {Fast Lattice Green's Function Methods for Viscous Incompressible Flows on Unbounded Domains},
  school = {California Institute of Technology},
  year = {2016},
  url = {http://resolver.caltech.edu/CaltechTHESIS:04062016-223108239}
}
Liska, S. and Colonius, T. A fast lattice Green's function method for solving viscous incompressible flows on unbounded domains 2016 Journal of Computational Physics
Vol. 316, pp. 360-384 
DOI URL 
Abstract: A computationally efficient method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. The method formally discretizes the incompressible Navier-Stokes equations on an unbounded staggered Cartesian grid. Operations are limited to a finite computational domain through a lattice Green's function technique. This technique obtains solutions to inhomogeneous difference equations through the discrete convolution of source terms with the fundamental solutions of the discrete-operators. The differential algebraic equations describing the temporal evolution of the discrete momentum equation and incompressibility constraint are numerically solved by combining an integrating factor technique for the viscous term and a half-explicit Runge-Kutta scheme for the convective term. A projection method that exploits the mimetic and commutativity properties of the discrete operators is used to efficiently solve the system of equations that arises in each stage of the time integration scheme. Linear complexity, fast computation rates, and parallel scalability are achieved using recently developed fast multipole methods for difference equations. The accuracy and physical fidelity of solutions are verified through numerical simulations of vortex rings.
BibTeX:
@article{LiskaColonius2016,
  author = {Liska, Sebastian and Colonius, Tim},
  title = {A fast lattice Green's function method for solving viscous incompressible flows on unbounded domains},
  journal = {Journal of Computational Physics},
  year = {2016},
  volume = {316},
  pages = {360-384},
  url = {http://colonius.caltech.edu/pdfs/LiskaColonius2016.pdf},
  doi = {https://doi.org/10.1016/j.jcp.2016.04.023}
}
Maeda, K., Colonius, T., Kreider, W., Maxwell, A. and Bailey, M. Modeling and experimental analysis of acoustic cavitation bubble clouds for burst-wave lithotripsy 2016 5th Joint Meeting of the Acoustical Society of America and the Acoustical Society of Japan  DOI  
BibTeX:
@inproceedings{MaedaColoniusKriederEtAl2016,
  author = {Maeda, K. and Colonius, T. and Kreider, W. and Maxwell, A. and Bailey, M.},
  title = {Modeling and experimental analysis of acoustic cavitation bubble clouds for burst-wave lithotripsy},
  booktitle = {5th Joint Meeting of the Acoustical Society of America and the Acoustical Society of Japan},
  year = {2016},
  doi = {https://doi.org/10.1121/1.4970532}
}
Meng, J. Numerical Simulations of Droplet Aerobreakup 2016 School: California Institute of Technology  URL 
Abstract: The work presented in this thesis aims to bridge an existing gap in the state of droplet aerobreakup knowledge associated with the fundamental flow physics that govern the experimentally observable droplet morphologies. Using direct numerical simulations of the aerobreakup of water cylinders and droplets in the flow behind shock waves in air, we investigate the behavior of the surrounding gas flow to gain insight into the droplet?s deformation and evolution in the stripping breakup regime. The compressible multicomponent Navier-Stokes equations are solved using the Multicomponent Flow Code -- a high-order accurate structured finite-volume flow solver with shock- and interface-capturing. Following qualitative descriptions of the aerobreakup process, comparisons are made with available experimental data. In 2D, accurate measurements of the cylinder?s center-of-mass acceleration across a range of incident shock Mach numbers allow characterization of the unsteady drag coefficient. Additionally, mass loss measurements from viscous simulations refute a well-known boundary layer stripping theory. The results of a 3D nonaxisymmetric aerobreakup simulation are presented with an emphasis on describing the intricate flow phenomena observable in the wake region. Subsequent analyses of the surface instabilities and a Fourier decomposition of the flow field reveal asymmetrical azimuthal modulations and broadband instability growth that result in the devolution of the wake region into chaotic flow.
BibTeX:
@phdthesis{Meng2016,
  author = {Jomela Meng},
  title = {Numerical Simulations of Droplet Aerobreakup},
  school = {California Institute of Technology},
  year = {2016},
  url = {http://resolver.caltech.edu/CaltechTHESIS:05262016-092840941}
}
Schmid, O., Colonius, T. and Brès, G. Modeling the generation of supersonic turbulent jet noise by large-scale coherent structures 2016 5th Joint Meeting of the Acoustical Society of America and the Acoustical Society of Japan  DOI  
BibTeX:
@inproceedings{SchmidtColoniusBres2016,
  author = {Schmid, O.T. and Colonius, T. and Brès, G.},
  title = {Modeling the generation of supersonic turbulent jet noise by large-scale coherent structures},
  booktitle = {5th Joint Meeting of the Acoustical Society of America and the Acoustical Society of Japan},
  year = {2016},
  doi = {https://doi.org/10.1121/1.4969657}
}
Schmidt, O., Towne, A., Colonius, T., Jordan, P., Jaunet, V., Cavalieri, A.V. and Brès, G.A. Super- and multi-directive acoustic radiation by linear global modes of a turbulent jet 2016 22nd AIAA/CEAS Aeroacoustics Conference  DOI URL 
BibTeX:
@inproceedings{SchmidtTowneColoniusEtAl2016,
  author = {Oliver Schmidt and Aaron Towne and Tim Colonius and Peter Jordan and Vincent Jaunet and André V. Cavalieri and Guillaume A. Brès},
  title = {Super- and multi-directive acoustic radiation by linear global modes of a turbulent jet},
  booktitle = {22nd AIAA/CEAS Aeroacoustics Conference},
  publisher = {American Institute of Aeronautics and Astronautics (AIAA)},
  year = {2016},
  url = {http://colonius.caltech.edu/pdfs/SchmidtTowneColoniusEtAl2016.pdf},
  doi = {https://doi.org/10.2514/6.2016-2808}
}
Sinha, A., Guðmundsson, K., Xia, H. and Colonius, T. Parabolized stability analysis of jets from serrated nozzles 2016 Journal of Fluid Mechanics
Vol. 789, pp. 36-63 
DOI URL 
Abstract: We study the viscous spatial linear stability characteristics of the time-averaged flow in turbulent subsonic jets issuing from serrated (chevroned) nozzles, and compare them to analogous round jet results. Linear parabolized stability equations (PSE) are used in the calculations to account for the non-parallel base flow. By exploiting the symmetries of the mean flow due to the regular arrangement of serrations, we obtain a series of coupled two-dimensional PSE problems from the original three-dimensional problem. This reduces the solution cost and manifests the symmetries of the stability modes. In the parallel-flow linear stability theory (LST) calculations that are performed near the nozzle to initiate the PSE, we find that the serrated nozzle reduces the growth rates of the most unstable eigenmodes of the jet, but their phase speeds are approximately similar. We obtain encouraging validation of our linear PSE instability wave results vis-a-vis near-field hydrodynamic pressure data acquired on a phased microphone array in experiments, after filtering the latter with proper orthogonal decomposition (POD) to extract the energetically dominant coherent part. Additionally, a large-eddy simulation database of the same serrated jet is investigated, and its POD-filtered pressure field is found to compare favourably with the corresponding PSE solution within the jet plume. We conclude that the coherent hydrodynamic pressure fluctuations of jets from both round and serrated nozzles are reasonably consistent with the linear instability modes of the turbulent mean flow.
BibTeX:
@article{SinhaGudmundssonXiaEtAl2016,
  author = {Sinha, Aniruddha and Guðmundsson, Kristjan and Xia, Hao and Colonius, Tim},
  title = {Parabolized stability analysis of jets from serrated nozzles},
  journal = {Journal of Fluid Mechanics},
  year = {2016},
  volume = {789},
  pages = {36-63},
  url = {http://colonius.caltech.edu/pdfs/SinhaGudmundssonXiaEtAl2016.pdf},
  doi = {https://doi.org/10.1017/jfm.2015.719}
}
Towne, A. Advancements in jet turbulence and noise modeling: accurate one-way solutions and empirical evaluation of the nonlinear forcing of wavepackets 2016 School: California Institute of Technology  URL 
Abstract: Jet noise reduction is an important goal within both commercial and military aviation. Although large-scale numerical simulations are now able to simultaneously compute turbulent jets and their radiated sound, lost-cost, physically-motivated models are needed to guide noise-reduction efforts. A particularly promising modeling approach centers around certain large-scale coherent structures, called wavepackets, that are observed in jets and their radiated sound. The typical approach to modeling wavepackets is to approximate them as linear modal solutions of the Euler or Navier-Stokes equations linearized about the long-time mean of the turbulent flow field. The near-field wavepackets obtained from these models show compelling agreement with those educed from experimental and simulation data for both subsonic and supersonic jets, but the acoustic radiation is severely under-predicted in the subsonic case. This thesis contributes to two aspects of these models. First, two new solution methods are developed that can be used to efficiently compute wavepackets and their acoustic radiation, reducing the computational cost of the model by more than an order of magnitude. The new techniques are spatial integration methods and constitute a well-posed, convergent alternative to the frequently used parabolized stability equations. Using concepts related to well-posed boundary conditions, the methods are formulated for general hyperbolic equations and thus have potential applications in many fields of physics and engineering. Second, the nonlinear and stochastic forcing of wavepackets is investigated with the goal of identifying and characterizing the missing dynamics responsible for the under-prediction of acoustic radiation by linear wavepacket models for subsonic jets. Specifically, we use ensembles of large-eddy-simulation flow and force data along with two data decomposition techniques to educe the actual nonlinear forcing experienced by wavepackets in a Mach 0.9 turbulent jet. Modes with high energy are extracted using proper orthogonal decomposition, while high gain modes are identified using a novel technique called empirical resolvent-mode decomposition. In contrast to the flow and acoustic fields, the forcing field is characterized by a lack of energetic coherent structures. Furthermore, the structures that do exist are largely uncorrelated with the acoustic field. Instead, the forces that most efficiently excite an acoustic response appear to take the form of random turbulent fluctuations, implying that direct feedback from nonlinear interactions amongst wavepackets is not an essential noise source mechanism. This suggests that the essential ingredients of sound generation in high Reynolds number jets are contained within the linearized Navier-Stokes operator rather than in the nonlinear forcing terms, a conclusion that has important implications for jet noise modeling.
BibTeX:
@phdthesis{Towne2016,
  author = {Aaron Towne},
  title = {Advancements in jet turbulence and noise modeling: accurate one-way solutions and empirical evaluation of the nonlinear forcing of wavepackets},
  school = {California Institute of Technology},
  year = {2016},
  url = {http://resolver.caltech.edu/CaltechTHESIS:01062016-163653523}
}
Towne, A., Cavalieri, A.V., Jordan, P., Colonius, T., Jaunet, V., Schmidt, O. and Brès, G.A. Trapped acoustic waves in the potential core of subsonic jets 2016 22nd AIAA/CEAS Aeroacoustics Conference  DOI URL 
BibTeX:
@inproceedings{TowneCavalieriJordanEtAl2016,
  author = {Aaron Towne and André V. Cavalieri and Peter Jordan and Tim Colonius and Vincent Jaunet and Oliver Schmidt and Guillaume A. Brès},
  title = {Trapped acoustic waves in the potential core of subsonic jets},
  booktitle = {22nd AIAA/CEAS Aeroacoustics Conference},
  publisher = {American Institute of Aeronautics and Astronautics (AIAA)},
  year = {2016},
  url = {http://colonius.caltech.edu/pdfs/TowneCavalieriJordanEtAl2016.pdf},
  doi = {https://doi.org/10.2514/6.2016-2809}
}
Tsai, H.-C. Numerical Investigation of Vertical-Axis Wind Turbines at Low Reynolds Number 2016 School: California Institute of Technology  URL 
Abstract: This thesis is aimed at numerically investigating the aerodynamics and the starting of a vertical-axis wind turbine at low Reynolds number using the immersed boundary method. The influence of the Coriolis effect on dynamic stall is isolated by comparing the rotating airfoil to one undergoing an equivalent planar motion that is composed of surging and pitching motions that produce an equivalent speed and angle of attack variation over a cycle. At lower tip-speed ratios, the Coriolis force leads to the capture of a vortex pair which results in a significant decrease in lift when the angle of attack of a rotating airfoil begins to decrease in the upwind half cycle. In the absence of the wake-capturing, the equivalent planar motion is a good approximation to a rotating blade in a vertical-axis wind turbine.

Analysis on the starting torque shows that when the turbine solidity is lower than about 0.5, the starting torque distribution can be well-modeled by considering a single blade at different orientations, and starting torque distributions for multi-bladed turbines can be constructed by linearly combining the torques at the respective positions of the blades. Using this model, optimal configurations to start a multi-bladed low-solidity vertical-axis wind turbine is proposed.

A preliminary study is made to determine an optimal blade pitch for a single-bladed motor-driven turbine using optimal control theory. When the input power is minimized directly, the solution seems to converge to only a local minimum due to a lower input power reduction than that obtained by maximizing the mean tangential force. After a transient, both controls converge to time-invariant pitch angles of about the same magnitude but with opposite signs. The wake-capturing phenomenon observed in the uncontrolled case necessitates large input power. Under active control, the disappearance of wake-capturing and attendant changes in the flow field collectively result in a reduction of required input power.

BibTeX:
@phdthesis{Tsai2016,
  author = {Hsieh-Chen Tsai},
  title = {Numerical Investigation of Vertical-Axis Wind Turbines at Low Reynolds Number},
  school = {California Institute of Technology},
  year = {2016},
  url = {http://resolver.caltech.edu/CaltechTHESIS:05272016-150613633}
}
Tsai, H.-C. and Colonius, T. Coriolis Effect on Dynamic Stall in a Vertical Axis Wind Turbine 2016 AIAA Journal
Vol. 54(1), pp. 216-226 
DOI URL 
Abstract: The immersed boundary method is used to simulate the flow around a two-dimensional cross section of a rotating NACA 0018 airfoil in order to investigate the dynamic stall occurring on a vertical axis wind turbine. The influence of dynamic stall on the force is characterized as a function of tip-speed ratio and Rossby number. The influence of the Coriolis effect is isolated by comparing the rotating airfoil to one undergoing an equivalent planar motion that is composed of surging and pitching motions that produce an equivalent speed and angle-of-attack variation over the cycle. Planar motions consisting of sinusoidally varying pitch and surge are also examined. At lower tip-speed ratios, the Coriolis force leads to the capture of a vortex pair when the angle of attack of a rotating airfoil begins to decrease in the upwind half cycle. This wake-capturing phenomenon leads to a significant decrease in lift during the downstroke phase. The appearance of this feature depends subtly on the tip-speed ratio. On the one hand, it is strengthened due to the intensifying Coriolis force, but on the other hand, it is attenuated because of the comitant decrease in angle of attack. While the present results are restricted to two-dimensional flow at low Reynolds numbers, they compare favorably with experimental observations at much higher Reynolds numbers. Moreover, the wake-capturing is observed only when the combination of surging, pitching, and Coriolis force is present.
BibTeX:
@article{TsaiColonius2016,
  author = {Tsai, Hsieh-Chen and Colonius, Tim},
  title = {Coriolis Effect on Dynamic Stall in a Vertical Axis Wind Turbine},
  journal = {AIAA Journal},
  year = {2016},
  volume = {54},
  number = {1},
  pages = {216-226},
  url = {http://colonius.caltech.edu/pdfs/TsaiColonius2016.pdf},
  doi = {https://doi.org/10.2514/1.j054199}
}
Tsai, H.-C. and Colonius, T. Numerical Investigation of Self-Starting Capability of Vertical-Axis Wind Turbines at Low Reynolds Numbers 2016 34th AIAA Applied Aerodynamics Conference  DOI URL 
BibTeX:
@inproceedings{TsaiColonius2016a,
  author = {Hsieh-Chen Tsai and Tim Colonius},
  title = {Numerical Investigation of Self-Starting Capability of Vertical-Axis Wind Turbines at Low Reynolds Numbers},
  booktitle = {34th AIAA Applied Aerodynamics Conference},
  publisher = {American Institute of Aeronautics and Astronautics (AIAA)},
  year = {2016},
  url = {http://colonius.caltech.edu/pdfs/TsaiColonius2016a.pdf},
  doi = {https://doi.org/10.2514/6.2016-3731}
}
Brès, G., Jaunet, V., Le Rallic, M., Jordan, P., Colonius, T. and Lele, S.K. Large eddy simulation for jet noise: the importance of getting the boundary layer right 2015 21st AIAA/CEAS Aeroacoustics Conference  DOI URL 
BibTeX:
@inproceedings{BresJaunetLeRallicEtAl2015,
  author = {Brès, Guillaume and Jaunet, Vincent and Le Rallic, Maxime and Jordan, Peter and Colonius, Tim and Lele, Sanjiva K.},
  title = {Large eddy simulation for jet noise: the importance of getting the boundary layer right},
  booktitle = {21st AIAA/CEAS Aeroacoustics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2015},
  url = {http://colonius.caltech.edu/pdfs/BresJaunetLeRallicEtAl2015.pdf},
  doi = {https://doi.org/10.2514/6.2015-2535}
}
Choi, J., Colonius, T. and Williams, D.R. Surging and plunging oscillations of an airfoil at low Reynolds number 2015 Journal of Fluid Mechanics
Vol. 763, pp. 237-253 
DOI URL 
Abstract: We investigate the forces and unsteady flow structures associated with harmonic oscillations of an airfoil in the streamwise (surging) and transverse (plunging) directions in two-dimensional simulations at low Reynolds number. For the surging case, we show that there are specific frequencies where the wake instability synchronizes with the unsteady motion of the airfoil, leading to significant changes in the mean forces. Resonant behaviour of the time-averaged forces is observed near the vortex shedding frequency and its subharmonic; the behaviour is reminiscent of the dynamics of the generic nonlinear oscillator known as the Arnol'd tongue or the resonance horn. Below the wake instability frequency, there are two regimes where the fluctuating forces are amplified and attenuated, respectively. A detailed study of the flow structures associated with leading-edge vortex (LEV) growth and detachment are used to relate this behaviour with the LEV acting either in phase with the quasi-steady component of the forces for the amplification case, or out of phase for the attenuation case. Comparisons with wind tunnel measurements show that phenomenologically similar dynamics occur at higher Reynolds number. Finally, we show that qualitatively similar phenomena occur during both surging and plunging.
BibTeX:
@article{ChoiColoniusWilliams2015,
  author = {Choi, J. and Colonius, T. and Williams, D. R.},
  title = {Surging and plunging oscillations of an airfoil at low Reynolds number},
  journal = {Journal of Fluid Mechanics},
  year = {2015},
  volume = {763},
  pages = {237-253},
  url = {http://colonius.caltech.edu/pdfs/ChoiColoniusWilliams2015.pdf},
  doi = {https://doi.org/10.1017/jfm.2014.674}
}
Colonius, T., Sinha, A., Rodr\iguez, D., Towne, A., Liu, J., Brès, G., Appelö, D. and Hagstrom, T. Simulation and Modeling of Turbulent Jet Noise 2015 Direct and Large-Eddy Simulation IX, pp. 305-310  DOI URL 
BibTeX:
@inproceedings{ColoniusSinhaRodriguezEtAl2015,
  author = {Colonius, T and Sinha, A and Rodr\iguez, D and Towne, A and Liu, J and Brès, GA and Appelö, D and Hagstrom, T},
  title = {Simulation and Modeling of Turbulent Jet Noise},
  booktitle = {Direct and Large-Eddy Simulation IX},
  publisher = {Springer},
  year = {2015},
  pages = {305-310},
  url = {http://colonius.caltech.edu/pdfs/ColoniusSinhaRodriguezEtAl2015.pdf},
  doi = {https://doi.org/10.1007/978-3-319-14448-1_38}
}
Coralic, V. Simulation of shock-induced bubble collapse with application to vascular injury in shockwave lithotripsy 2015 School: California Institute of Technology  URL 
Abstract: Shockwave lithotripsy is a noninvasive medical procedure wherein shockwaves are repeatedly focused at the location of kidney stones in order to pulverize them. Stone comminution is thought to be the product of two mechanisms: the propagation of stress waves within the stone and cavitation erosion. However, the latter mechanism has also been implicated in vascular injury. In the present work, shock-induced bubble collapse is studied in order to understand the role that it might play in inducing vascular injury. A high-order accurate, shock- and interface-capturing numerical scheme is developed to simulate the three-dimensional collapse of the bubble in both the free-field and inside a vessel phantom. The primary contributions of the numerical study are the characterization of the shock-bubble and shock-bubble-vessel interactions across a large parameter space that includes clinical shockwave lithotripsy pressure amplitudes, problem geometry and tissue viscoelasticity, and the subsequent correlation of these interactions to vascular injury. Specifically, measurements of the vessel wall pressures and displacements, as well as the finite strains in the fluid surrounding the bubble, are utilized with available experiments in tissue to evaluate damage potential. Estimates are made of the smallest injurious bubbles in the microvasculature during both the collapse and jetting phases of the bubble's life cycle. The present results suggest that bubbles larger than 1 μ m in diameter could rupture blood vessels under clinical SWL conditions.
BibTeX:
@phdthesis{Coralic2015,
  author = {Coralic, Vedran},
  title = {Simulation of shock-induced bubble collapse with application to vascular injury in shockwave lithotripsy},
  school = {California Institute of Technology},
  year = {2015},
  url = {http://resolver.caltech.edu/CaltechTHESIS:01222015-234921548}
}
Dunne, R., Tsai, H.-C., Colonius, T. and McKeon, B. Leading edge vortex development on pitching and surging airfoils: A study of vertical axis wind turbines 2015 International Conference on Wakes, Jets and Separated flows, Stockholm, Sweden  URL 
BibTeX:
@inproceedings{DunneTsaiColoniusEtAl2015,
  author = {Dunne, R. and Tsai, H.-C. and Colonius, T. and McKeon, B.J.},
  title = {Leading edge vortex development on pitching and surging airfoils: A study of vertical axis wind turbines},
  booktitle = {International Conference on Wakes, Jets and Separated flows, Stockholm, Sweden},
  year = {2015},
  url = {http://colonius.caltech.edu/pdfs/DunneTsaiColoniusEtAl2015.pdf}
}
Flinois, T.L.B. and Colonius, T. Optimal control of circular cylinder wakes using long control horizons 2015 Physics of Fluids
Vol. 27(8) 
DOI URL 
Abstract: The classical problem of suppressing vortex shedding in the wake of a circular cylinder by using body rotation is revisited in an adjoint-based optimal control framework. The cylinder's unsteady and fully unconstrained rotation rate is optimized at Reynolds numbers between 75 and 200 and over horizons that are longer than in previous studies, where they are typically of the order of a vortex shedding period or shorter. In the best configuration, the drag is reduced by 19%, the vortex shedding is effectively suppressed, and this low drag state is maintained with minimal cylinder rotation after transients. Unlike open-loop control, the optimal control is shown to maintain a specific phase relationship between the actuation and the shedding in order to stabilize the wake. A comparison is also given between the performance of optimizations for different Reynolds numbers, cost functions, and horizon lengths. It is shown that the long horizons used are necessary in order to stabilize the vortex shedding efficiently.
BibTeX:
@article{FlinoisColonius2015,
  author = {Flinois, T. L. B. and Colonius, T.},
  title = {Optimal control of circular cylinder wakes using long control horizons},
  journal = {Physics of Fluids},
  year = {2015},
  volume = {27},
  number = {8},
  url = {http://colonius.caltech.edu/pdfs/FlinoisColonius2015.pdf},
  doi = {https://doi.org/10.1063/1.4928896}
}
Lee, H., Sherrit, S., Tosi, L.P., Walkemeyer, P. and Colonius, T. Piezoelectric Energy Harvesting in Internal Fluid Flow 2015 Sensors
Vol. 15(10), pp. 26039-26062 
DOI URL 
Abstract: We consider piezoelectric flow energy harvesting in an internal flow environment with the ultimate goal powering systems such as sensors in deep oil well applications. Fluid motion is coupled to structural vibration via a cantilever beam placed in a converging-diverging flow channel. Two designs were considered for the electromechanical coupling: first; the cantilever itself is a piezoelectric bimorph; second; the cantilever is mounted on a pair of flextensional actuators. We experimentally investigated varying the geometry of the flow passage and the flow rate. Experimental results revealed that the power generated from both designs was similar; producing as much as 20 mW at a flow rate of 20 L/min. The bimorph designs were prone to failure at the extreme of flow rates tested. Finite element analysis (FEA) showed fatigue failure was imminent due to stress concentrations near the bimorph's clamped region; and that robustness could be improved with a stepped-joint mounting design. A similar FEA model showed the flextensional-based harvester had a resonant frequency of around 375 Hz and an electromechanical coupling of 0.23 between the cantilever and flextensional actuators in a vacuum. These values; along with the power levels demonstrated; are significant steps toward building a system design that can eventually deliver power in the Watts range to devices down within a well.
BibTeX:
@article{LeeSherritTosiEtAl2015,
  author = {Lee, H.J. and Sherrit, S. and Tosi, L. P. and Walkemeyer, P. and Colonius, T.},
  title = {Piezoelectric Energy Harvesting in Internal Fluid Flow},
  journal = {Sensors},
  year = {2015},
  volume = {15},
  number = {10},
  pages = {26039-26062},
  url = {http://colonius.caltech.edu/pdfs/LeeSherritTosiEtAl2015.pdf},
  doi = {https://doi.org/10.3390/s151026039}
}
Maeda, K., Kreider, W., Maxwell, A., Cunitz, B., Colonius, T. and Bailey, M. Modeling and experimental analysis of acoustic cavitation bubbles for Burst Wave Lithotripsy 2015 J. Phys.: Conf. Ser.
Vol. 656, pp. 012027 
DOI URL 
Abstract: Cavitation bubbles initiated by focused ultrasound waves are investigated through experiments and modeling. Pulses of focused ultrasound with a frequency of 335 kHz and a peak negative pressure of 8 MPa is generated in a water tank by a piezoelectric transducer to
initiate cavitation. The pressure field is modeled by solving the Euler equations and used to simulate single bubble oscillation. The characteristics of cavitation bubbles observed by highspeed photography qualitatively agree with the simulation results. Finally, bubble clouds are captured using acoustic B-mode imaging that works synchronized with high-speed photography.
BibTeX:
@article{MaedaKreiderMaxwellEtAl2015,
  author = {Kazuki Maeda and Wayne Kreider and Adam Maxwell and Bryan Cunitz and Tim Colonius and Michael Bailey},
  title = {Modeling and experimental analysis of acoustic cavitation bubbles for Burst Wave Lithotripsy},
  journal = {J. Phys.: Conf. Ser.},
  year = {2015},
  volume = {656},
  pages = {012027},
  url = {http://colonius.caltech.edu/pdfs/MaedaKreiderMaxwellEtAl2015.pdf},
  doi = {https://doi.org/10.1088/1742-6596/656/1/012027}
}
Meng, J.C. and Colonius, T. Numerical simulations of the early stages of high-speed droplet breakup 2015 Shock Waves
Vol. 25(4), pp. 399-414 
DOI URL 
Abstract: Experiments reported in the literature are reproduced using numerical simulations to investigate the early stages of the breakup of water cylinders in the flow behind normal shocks. Qualitative features of breakup observed in the numerical results, such as the initial streamwise flattening of the cylinder and the formation of tips at its periphery, support previous experimental observations of stripping breakup. Additionally, the presence of a transitory recirculation region at the cylinder's equator and a persistent upstream jet in the wake is noted and discussed. Within the uncertainties inherent to the different methods used to extract measurements from experimental and numerical results, comparisons with experimental data of various cylinder deformation metrics show good agreement. To study the effects of the transition between subsonic and supersonic post-shock flow, we extend the range of incident shock Mach numbers beyond those investigated by the experiments. Supersonic post-shock flow velocities are not observed to significantly alter the cylinder's behavior, i.e., we are able to effectively collapse the drift, acceleration, and drag curves for all simulated shock Mach numbers. Using a new method that minimizes noise errors, the cylinder's acceleration is calculated; acceleration curves for all shock Mach numbers are subsequently collapsed by scaling with the pressure ratio across the incident shock. Furthermore, we find that accounting for the cylinder's deformed diameter in the calculation of its unsteady drag coefficient allows the drag coefficient to be approximated as a constant over the initial breakup period.
BibTeX:
@article{MengColonius2015,
  author = {Meng, J. C. and Colonius, T.},
  title = {Numerical simulations of the early stages of high-speed droplet breakup},
  journal = {Shock Waves},
  year = {2015},
  volume = {25},
  number = {4},
  pages = {399-414},
  url = {http://colonius.caltech.edu/pdfs/MengColonius2015.pdf},
  doi = {https://doi.org/10.1007/s00193-014-0546-z}
}
Rodríguez, D., Cavalieri, A.V.G., Colonius, T. and Jordan, P. A study of linear wavepacket models for subsonic turbulent jets using local eigenmode decomposition of PIV data 2015 European Journal of Mechanics B-Fluids
Vol. 49, pp. 308-321 
DOI URL 
Abstract: Locally-parallel linear stability theory (LST) of jet velocity profiles is revisited to study the evolution of the wavepackets and the manner in which the parabolized stability equations (PSE) approach models them. An adjoint-based eigenmode decomposition technique is used to project cross-sectional velocity profiles measured using time-resolved particle image velocimetry (PIV) on the different families of eigenmodes present in the LST eigenspectrum. Attention is focused on the evolution of the Kelvin-Helmholtz (K-H) eigenmode and the projection of experimental fluctuations on it, since in subsonic jets the inflectional K H instability is the only possible mechanism for linear amplification of the large-scale fluctuations, and governs the wavepacket evolution. Comparisons of the fluctuations extracted by projection onto K-H eigenmode with PSE solutions and Ply measurements are made. We show that the jet can be divided into three main regions, classified with respect to the LST eigenspectrum. Near the jet exit, there is significant amplification of the K-H mode; the PSE solution is shown to comprise almost exclusively the K-H mode, and the agreement with experiments shows that the evolution of this mode dominates the near-nozzle fluctuations. For downstream positions, the Kelvin-Helmholtz mode becomes stable and eventually merges with other branches of the eigenspectrum. The comparison between PSE, experiment and the projection onto the K-H mode for downstream positions suggests that the mechanism of saturation and decay of wavepackets is related to a combination of several marginally stable modes, which is reasonably well modeled by linear PSE, but cannot be obtained in the usual application of locally-parallel stability dealing exclusively with the K-H mode. In addition, the projection of empirical data on the K-H eigenmode at a near-nozzle cross-section is shown to be a well-founded method for the determination of the amplitudes of the linear wavepacket models.
BibTeX:
@article{RodriguezCavalieriColoniusEtAl2015,
  author = {Rodríguez, D. and Cavalieri, A. V. G. and Colonius, T. and Jordan, P.},
  title = {A study of linear wavepacket models for subsonic turbulent jets using local eigenmode decomposition of PIV data},
  journal = {European Journal of Mechanics B-Fluids},
  year = {2015},
  volume = {49},
  pages = {308-321},
  url = {http://colonius.caltech.edu/pdfs/RodriguezCavalieriColoniusEtAl2015.pdf},
  doi = {https://doi.org/10.1016/j.euromechflu.2014.03.004}
}
Sherrit, S., Lee, H.J., Walkemeyer, P., Winn, T., Tosi, L.P. and Colonius, T. Fluid flow nozzle energy harvesters 2015 Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2015  DOI URL 
Abstract: Power generation schemes that could be used downhole in an oil well to produce about 1 Watt average power with long-life (decades) are actively being developed. A variety of proposed energy harvesting schemes could be used to extract energy from this environment but each of these has their own limitations that limit their practical use. Since vibrating piezoelectric structures are solid state and can be driven below their fatigue limit, harvesters based on these structures are capable of operating for very long lifetimes (decades); thereby, possibly overcoming a principle limitation of existing technology based on rotating turbo-machinery. An initial survey [1] identified that spline nozzle configurations can be used to excite a vibrating piezoelectric structure in such a way as to convert the abundant flow energy into useful amounts of electrical power. This paper presents current flow energy harvesting designs and experimental results of specific spline nozzle/ bimorph design configurations which have generated suitable power per nozzle at or above well production analogous flow rates. Theoretical models for non-dimensional analysis and constitutive electromechanical model are also presented in this paper to optimize the flow harvesting system.
BibTeX:
@inproceedings{SherritLeeWalkemeyerEtAl2015,
  author = {Sherrit, S. and Lee, H. J. and Walkemeyer, P. and Winn, T. and Tosi, L. P. and Colonius, T.},
  title = {Fluid flow nozzle energy harvesters},
  booktitle = {Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2015},
  year = {2015},
  url = {http://colonius.caltech.edu/pdfs/SherritLeeWalkemeyerEtAl2015.pdf},
  doi = {https://doi.org/10.1117/12.2084574}
}
Sinha, A. and Colonius, T. Linear Stability Implications of Mean Flow Variations in Turbulent Jets Issuing from Serrated Nozzles 2015 21st AIAA/CEAS Aeroacoustics Conference  DOI URL 
BibTeX:
@inproceedings{SinhaColonius2015,
  author = {Sinha, Aniruddha and Colonius, Tim},
  title = {Linear Stability Implications of Mean Flow Variations in Turbulent Jets Issuing from Serrated Nozzles},
  booktitle = {21st AIAA/CEAS Aeroacoustics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2015},
  url = {http://colonius.caltech.edu/pdfs/SinhaColonius2015.pdf},
  doi = {https://doi.org/10.2514/6.2015-3125}
}
Sinha, A., Xia, H. and Colonius, T. Parbolized Stability Analysis of Jets Issuing from Serrated Nozzles 2015 3rd Symposium on FSSIC  DOI URL 
BibTeX:
@inproceedings{SinhaXiaColonius2015,
  author = {Sinha, A and Xia, H and Colonius, T},
  title = {Parbolized Stability Analysis of Jets Issuing from Serrated Nozzles},
  booktitle = {3rd Symposium on FSSIC},
  year = {2015},
  url = {http://colonius.caltech.edu/pdfs/SinhaXiaColonius2015.pdf},
  doi = {https://doi.org/10.1007/978-3-662-48868-3_34}
}
Tissot, G., Zhang, M., Lajús, F., Cavalieri, A., Jordan, P. and Colonius, T. Sensitivity of wavepackets in jets to non-linear effects: the role of the critical layer 2015 21st AIAA/CEAS Aeroacoustics Conference  DOI URL 
BibTeX:
@inproceedings{TissotZhangLajusEtAl2015,
  author = {Tissot, Gilles and Zhang, Mengqi and Lajús, Francisco and Cavalieri, André and Jordan, Peter and Colonius, Tim},
  title = {Sensitivity of wavepackets in jets to non-linear effects: the role of the critical layer},
  booktitle = {21st AIAA/CEAS Aeroacoustics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2015},
  url = {http://colonius.caltech.edu/pdfs/TissotZhangLajusEtAl2015.pdf},
  doi = {https://doi.org/10.2514/6.2015-2218}
}
Towne, A. and Colonius, T. One-way spatial integration of hyperbolic equations 2015 Journal of Computational Physics
Vol. 300, pp. 844-861 
DOI URL 
Abstract: In this paper, we develop and demonstrate a method for constructing well-posed one-way approximations of linear hyperbolic systems. We use a semi-discrete approach that allows the method to be applied to a wider class of problems than existing methods based on analytical factorization of idealized dispersion relations. After establishing the existence of an exact one-way equation for systems whose coefficients do not vary along the axis of integration, efficient approximations of the one-way operator are constructed by generalizing techniques previously used to create nonreflecting boundary conditions. When physically justified, the method can be applied to systems with slowly varying coefficients in the direction of integration. To demonstrate the accuracy and computational efficiency of the approach, the method is applied to model problems in acoustics and fluid dynamics via the linearized Euler equations; in particular we consider the scattering of sound waves from a vortex and the evolution of hydrodynamic wavepackets in a spatially evolving jet. The latter problem shows the potential of the method to offer a systematic, convergent alternative to ad hoc regularizations such as the parabolized stability equations.
BibTeX:
@article{TowneColonius2015,
  author = {Towne, Aaron and Colonius, Tim},
  title = {One-way spatial integration of hyperbolic equations},
  journal = {Journal of Computational Physics},
  year = {2015},
  volume = {300},
  pages = {844-861},
  url = {http://colonius.caltech.edu/pdfs/TowneColonius2015.pdf},
  doi = {https://doi.org/10.1016/j.jcp.2015.08.015}
}
Towne, A., Colonius, T., Jordan, P., Cavalieri, A. and Brés, G. Stochastic and nonlinear forcing of wavepackets in a Mach 0.9 jet 2015 21st AIAA/CEAS Aeroacoustics Conference  DOI URL 
BibTeX:
@inproceedings{TowneColoniusJordanEtAl2015,
  author = {Towne, Aaron and Colonius, Tim and Jordan, Peter and Cavalieri, André and Brés, Guillaume},
  title = {Stochastic and nonlinear forcing of wavepackets in a Mach 0.9 jet},
  booktitle = {21st AIAA/CEAS Aeroacoustics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2015},
  url = {http://colonius.caltech.edu/pdfs/TowneColoniusJordanEtAl2015.pdf},
  doi = {https://doi.org/10.2514/6.2015-2217}
}
Uzun, A., Alvi, F.S., Colonius, T. and Hussaini, M.Y. Spatial Stability Analysis of Subsonic Jets Modified for Low-Frequency Noise Reduction 2015 AIAA Journal
Vol. 53(8), pp. 2335-2358 
DOI URL 
Abstract: This study performs a spatial stability analysis of several jets that have previously been investigated in terms of their noise radiation. The cases include a round jet and two chevron nozzle jets with varying penetration angle. The instability wave evolution in the near-nozzle region is examined to seek for clues as to how and why the mean flow azimuthal inhomogeneity introduced by chevrons modifies the low-frequency noise component. A biglobal stability analysis is performed to determine the most unstable modes on an initial plane. The downstream evolution of the most unstable modes is then computed via three-dimensional parabolized stability equations. The azimuthal mean flow inhomogeneity introduced by chevrons is found to modify instability wave growth rates and phase speeds. Findings indicate that the near-field hydrodynamic pressure oscillations of round jet instability modes are suppressed by chevron jets. For the same modal excitation amplitude at the inlet, the two chevron jets generate considerably lower pressure fluctuations than the round jet. It is also shown that the chevron jet with the lowest hydrodynamic pressure fluctuation levels is the jet with the lowest far-field low-frequency noise output among the three jets.
BibTeX:
@article{UzunAlviColoniusEtAl2015,
  author = {Uzun, Ali and Alvi, Farrukh S. and Colonius, Tim and Hussaini, M. Yousuff},
  title = {Spatial Stability Analysis of Subsonic Jets Modified for Low-Frequency Noise Reduction},
  journal = {AIAA Journal},
  year = {2015},
  volume = {53},
  number = {8},
  pages = {2335-2358},
  url = {http://colonius.caltech.edu/pdfs/UzunAlviColoniusEtAl2015.pdf},
  doi = {https://doi.org/10.2514/1.J053719}
}
Brès, G., Jordan, P., Colonius, T., Le Rallic, M., Jaunet, V. and Lele, S. Large-eddy simulation of a Mach 0.9 turbulent jet 2014 Proceedings of the 2014 Summer Program  URL 
BibTeX:
@inproceedings{BresJordanColoniusEtAl2014,
  author = {Brès, G. and Jordan, P. and Colonius, T. and Le Rallic, M. and Jaunet, V. and Lele, S.K.},
  title = {Large-eddy simulation of a Mach 0.9 turbulent jet},
  booktitle = {Proceedings of the 2014 Summer Program},
  publisher = {Center for Turbulence Research},
  year = {2014},
  url = {http://colonius.caltech.edu/pdfs/BresJordanColoniusEtAl2014.pdf}
}
Colonius, T., Towne, A., Schlinker, R.H., Reba, R.A. and Shannon, D. Active control of noise from hot, supersonic turbulent jets 2014 168th Meeting of the Acoustical Society of America  DOI  
BibTeX:
@inproceedings{ColoniusTowneSchlinkerEtAl2014,
  author = {Colonius, Tim and Towne, Aaron and Schlinker, Robert H. and Reba, Ramons A. and Shannon, Dan},
  title = {Active control of noise from hot, supersonic turbulent jets},
  booktitle = {168th Meeting of the Acoustical Society of America},
  year = {2014},
  doi = {https://doi.org/10.1121/1.4899469}
}
Coralic, V. and Colonius, T. Finite-volume WENO scheme for viscous compressible multicomponent flows 2014 Journal of Computational Physics
Vol. 274, pp. 95-121 
DOI URL 
Abstract: We develop a shock- and interface-capturing numerical method that is suitable for the simulation of multicomponent flows governed by the compressible Navier-Stokes equations. The numerical method is high-order accurate in smooth regions of the flow, discretely conserves the mass of each component, as well as the total momentum and energy, and is oscillation-free, i.e. it does not introduce spurious oscillations at the locations of shockwaves and/or material interfaces. The method is of Godunov-type and utilizes a fifth-order, finite-volume, weighted essentially non-oscillatory (WENO) scheme for the spatial reconstruction and a Harten-Lax-van Leer contact (HLLC) approximate Riemann solver to upwind the fluxes. A third-order total variation diminishing (TVD) Runge-Kutta (RK) algorithm is employed to march the solution in time. The derivation is generalized to three dimensions and nonuniform Cartesian grids. A two-point, fourth-order, Gaussian quadrature rule is utilized to build the spatial averages of the reconstructed variables inside the cells, as well as at cell boundaries. The algorithm is therefore fourth-order accurate in space and third-order accurate in time in smooth regions of the flow. We corroborate the properties of our numerical method by considering several challenging one-, two- and three-dimensional test cases, the most complex of which is the asymmetric collapse of an air bubble submerged in a cylindrical water cavity that is embedded in 10% gelatin.
BibTeX:
@article{CoralicColonius2014,
  author = {Coralic, V. and Colonius, T.},
  title = {Finite-volume WENO scheme for viscous compressible multicomponent flows},
  journal = {Journal of Computational Physics},
  year = {2014},
  volume = {274},
  pages = {95-121},
  url = {http://colonius.caltech.edu/pdfs/CoralicColonius2014.pdf},
  doi = {https://doi.org/10.1016/j.jcp.2014.06.003}
}
Coralic, V. and Colonius, T. Modeling vascular injury due to shock-induced bubble collapse in lithotripsy 2014 168th Meeting of the Acoustical Society of America  DOI  
BibTeX:
@inproceedings{CoralicColonius2014a,
  author = {Coralic, Vedran and Colonius, Tim},
  title = {Modeling vascular injury due to shock-induced bubble collapse in lithotripsy},
  booktitle = {168th Meeting of the Acoustical Society of America},
  year = {2014},
  doi = {https://doi.org/10.1121/1.4899946}
}
Fuster, D., Conoir, J.M. and Colonius, T. Effect of direct bubble-bubble interactions on linear-wave propagation in bubbly liquids 2014 Physical Review E
Vol. 90(6) 
DOI URL 
Abstract: We study the influence of bubble-bubble interactions on the propagation of linear acoustic waves in bubbly liquids. Using the full model proposed by Fuster and Colonius [J. Fluid Mech. 688, 253 ( 2011)], numerical simulations reveal that direct bubble-bubble interactions have an appreciable effect for frequencies above the natural resonance frequency of the average size bubble. Based on the new results, a modification of the classical wave propagation theory is proposed. The results obtained are in good agreement with previously reported experimental data where the classical linear theory systematically overpredicts the effective attenuation and phase velocity.
BibTeX:
@article{FusterConoirColonius2014,
  author = {Fuster, D. and Conoir, J. M. and Colonius, T.},
  title = {Effect of direct bubble-bubble interactions on linear-wave propagation in bubbly liquids},
  journal = {Physical Review E},
  year = {2014},
  volume = {90},
  number = {6},
  url = {http://colonius.caltech.edu/pdfs/FusterConoirColonius2014.pdf},
  doi = {https://doi.org/10.1103/Physreve.90.063010}
}
Jordan, P., Colonius, T., Brès, G., Zhang, M., Towne, A. and Lele, S. Modeling intermittent wavepackets and their radiated sound in a turbulent jet 2014 Proceedings of the 2014 Summer Program  URL 
BibTeX:
@inproceedings{JordanColoniusBresEtAl2014,
  author = {Jordan, P. and Colonius, T. and Brès, G. and Zhang, M. and Towne, A. and Lele, S.K.},
  title = {Modeling intermittent wavepackets and their radiated sound in a turbulent jet},
  booktitle = {Proceedings of the 2014 Summer Program},
  publisher = {Center for Turbulence Research},
  year = {2014},
  url = {http://colonius.caltech.edu/pdfs/JordanColoniusBresEtAl2014.pdf}
}
Liska, S. and Colonius, T. A parallel fast multipole method for elliptic difference equations 2014 Journal of Computational Physics
Vol. 278, pp. 76-91 
DOI URL 
Abstract: A new fast multipole formulation for solving elliptic difference equations on unbounded domains and its parallel implementation are presented. These difference equations can arise directly in the description of physical systems, e.g. crystal structures, or indirectly through the discretization of PDEs. In the analog to solving continuous inhomogeneous differential equations using Green's functions, the proposed method uses the fundamental solution of the discrete operator on an infinite grid, or lattice Green's function. Fast solutions O(N) are achieved by using a kernel-independent interpolation-based fast multipole method. Unlike other fast multipole algorithms, our approach exploits the regularity of the underlying Cartesian grid and the efficiency of FFTs to reduce the computation time. Our parallel implementation allows communications and computations to be overlapped and requires minimal global synchronization. The accuracy, efficiency, and parallel performance of the method are demonstrated through numerical experiments on the discrete 3D Poisson equation.
BibTeX:
@article{LiskaColonius2014,
  author = {Liska, S. and Colonius, T.},
  title = {A parallel fast multipole method for elliptic difference equations},
  journal = {Journal of Computational Physics},
  year = {2014},
  volume = {278},
  pages = {76-91},
  url = {http://colonius.caltech.edu/pdfs/LiskaColonius2014.pdf},
  doi = {https://doi.org/10.1016/j.jcp.2014.07.048}
}
Regele, J.D., Rabinovitch, J., Colonius, T. and Blanquart, G. Unsteady effects in dense, high speed, particle laden flows 2014 International Journal of Multiphase Flow
Vol. 61, pp. 1-13 
DOI URL 
Abstract: Dense high speed non-compacted multiphase flows exist in variable phase turbines, explosions, and ejector nozzles, where the particle volume fraction is in the range 0.001
BibTeX:
@article{RegeleRabinovitchColoniusEtAl2014,
  author = {Regele, J. D. and Rabinovitch, J. and Colonius, T. and Blanquart, G.},
  title = {Unsteady effects in dense, high speed, particle laden flows},
  journal = {International Journal of Multiphase Flow},
  year = {2014},
  volume = {61},
  pages = {1-13},
  url = {http://colonius.caltech.edu/pdfs/RegeleRabinovitchColoniusEtAl2014.pdf},
  doi = {https://doi.org/10.1016/j.ijmultiphaseflow.2013.12.007}
}
Sherrit, S., Lee, H.J., Walkemeyer, P., Hasenoehrl, J., Hall, J.L., Colonius, T., Tosi, L.P., Arrazola, A., Kim, N., Sun, K. and Corbett, G. Flow Energy Piezoelectric Bimorph Nozzle Harvester 2014 Active and Passive Smart Structures and Integrated Systems 2014  DOI URL 
Abstract: There is a need for a long-life power generation scheme that could be used downhole in an oil well to produce 1 Watt average power. There are a variety of existing or proposed energy harvesting schemes that could be used in this environment but each of these has its own limitations. The vibrating piezoelectric structure is in principle capable of operating for very long lifetimes (decades) thereby possibly overcoming a principle limitation of existing technology based on rotating turbo-machinery. In order to determine the feasibility of using piezoelectrics to produce suitable flow energy harvesting, we surveyed experimentally a variety of nozzle configurations that could be used to excite a vibrating piezoelectric structure in such a way as to enable conversion of flow energy into useful amounts of electrical power. These included reed structures, spring mass-structures, drag and lift bluff bodies and a variety of nozzles with varying flow profiles. Although not an exhaustive survey we identified a spline nozzle/piezoelectric bimorph system that experimentally produced up to 3.4 mW per bimorph. This paper will discuss these results and present our initial analyses of the device using dimensional analysis and constitutive electromechanical modeling. The analysis suggests that an order-of-magnitude improvement in power generation from the current design is possible.
BibTeX:
@inproceedings{SherritLeeWalkemeyerEtAl2014,
  author = {Sherrit, S. and Lee, H. J. and Walkemeyer, P. and Hasenoehrl, J. and Hall, J. L. and Colonius, T. and Tosi, L. P. and Arrazola, A. and Kim, N. and Sun, K. and Corbett, G.},
  title = {Flow Energy Piezoelectric Bimorph Nozzle Harvester},
  booktitle = {Active and Passive Smart Structures and Integrated Systems 2014},
  year = {2014},
  url = {http://colonius.caltech.edu/pdfs/SherritLeeWalkemeyerEtAl2014.pdf},
  doi = {https://doi.org/10.1117/12.2045191}
}
Sinha, A., Rodríguez, D., Brès, G.A. and Colonius, T. Wavepacket models for supersonic jet noise 2014 Journal of Fluid Mechanics
Vol. 742, pp. 71-95 
DOI URL 
Abstract: Guðmundsson and Colonius (J. Fluid Mech., vol. 689, 2011, pp. 97-128) have recently shown that the average evolution of low-frequency, low-azimuthal modal large-scale structures in the near field of subsonic jets are remarkably well predicted as linear instability waves of the turbulent mean flow using parabolized stability equations. In this work, we extend this modelling technique to an isothermal and a moderately heated Mach 1.5 jet for which the mean flow fields are obtained from a high-fidelity large-eddy simulation database. The latter affords a rigourous and extensive validation of the model, which had only been pursued earlier with more limited experimental data. A filter based on proper orthogonal decomposition is applied to the data to extract the most energetic coherent components. These components display a distinct wavepacket character, and agree fairly well with the parabolized stability equations model predictions in terms of near-field pressure and flow velocity. We next apply a Kirchhoff surface acoustic propagation technique to the near-field pressure model and obtain an encouraging match for far-field noise levels in the peak aft direction. The results suggest that linear wavepackets in the turbulence are responsible for the loudest portion of the supersonic jet acoustic field.
BibTeX:
@article{SinhaRodriguezBresEtAl2014,
  author = {Sinha, A. and Rodríguez, D. and Brès, G. A. and Colonius, T.},
  title = {Wavepacket models for supersonic jet noise},
  journal = {Journal of Fluid Mechanics},
  year = {2014},
  volume = {742},
  pages = {71-95},
  url = {http://colonius.caltech.edu/pdfs/SinhaRodriguezBresEtAl2014.pdf},
  doi = {https://doi.org/10.1017/jfm.2013.660}
}
Towne, A. and Colonius, T. Continued development of the one-way Euler equations: application to jets 2014 20th AIAA/CEAS Aeroacoustics Conference  DOI URL 
BibTeX:
@inproceedings{TowneColonius2014,
  author = {Towne, Aaron and Colonius, Tim},
  title = {Continued development of the one-way Euler equations: application to jets},
  booktitle = {20th AIAA/CEAS Aeroacoustics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2014},
  url = {http://colonius.caltech.edu/pdfs/TowneColonius2014.pdf},
  doi = {https://doi.org/10.2514/6.2014-2903}
}
Towne, A. and Colonius, T. Efficient jet noise models using the one-way Euler equations 2014 168th Meeting of the Acoustical Society of America  DOI  
BibTeX:
@inproceedings{TowneColonius2014a,
  author = {Towne, Aaron and Colonius, Tim},
  title = {Efficient jet noise models using the one-way Euler equations},
  booktitle = {168th Meeting of the Acoustical Society of America},
  year = {2014},
  doi = {https://doi.org/10.1121/1.4899470}
}
Tsai, H.-C. and Colonius, T. Coriolis Effect on Dynamic Stall in a Vertical Axis Wind Turbine at Moderate Reynolds Number 2014 32nd AIAA Applied Aerodynamics Conference  DOI URL 
BibTeX:
@inproceedings{TsaiColonius2014,
  author = {Tsai, Hsieh-Chen and Colonius, Tim},
  title = {Coriolis Effect on Dynamic Stall in a Vertical Axis Wind Turbine at Moderate Reynolds Number},
  booktitle = {32nd AIAA Applied Aerodynamics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2014},
  url = {http://colonius.caltech.edu/pdfs/TsaiColonius2014.pdf},
  doi = {https://doi.org/10.2514/6.2014-3140}
}
Ando, K., Colonius, T. and Brennen, C.E. Shock Propagation in Polydisperse Bubbly Liquids 2013 Bubble Dynamics and Shock Waves, pp. 141-175  DOI  
BibTeX:
@inbook{AndoColoniusBrennen2013,
  author = {Ando, Keita and Colonius, Tim and Brennen, Christopher E},
  title = {Shock Propagation in Polydisperse Bubbly Liquids},
  booktitle = {Bubble Dynamics and Shock Waves},
  publisher = {Springer},
  year = {2013},
  pages = {141-175},
  doi = {https://doi.org/10.1007/978-3-642-34297-4_5}
}
Breakey, D., Jordan, P., Cavalieri, A., Léon, O., Zhang, M., Lehnasch, G., Colonius, T. and Rodr\iguez, D. Near-field Wavepackets and the Far-field Sound of a Subsonic Jet 2013 19th AIAA/CEAS Aeroacoustics Conference  DOI URL 
BibTeX:
@inproceedings{BreakeyJordanCavalieriEtAl2013,
  author = {Breakey, David and Jordan, Peter and Cavalieri, André and Léon, Olivier and Zhang, Mengqi and Lehnasch, Guillaume and Colonius, Tim and Rodr\iguez, Daniel},
  title = {Near-field Wavepackets and the Far-field Sound of a Subsonic Jet},
  booktitle = {19th AIAA/CEAS Aeroacoustics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2013},
  url = {http://colonius.caltech.edu/pdfs/BreakeyJordanCavalieriEtAl2013.pdf},
  doi = {https://doi.org/10.2514/6.2013-2083}
}
Brès, G.A., Inkman, M., Colonius, T. and Fedorov, A.V. Second-mode attenuation and cancellation by porous coatings in a high-speed boundary layer 2013 Journal of Fluid Mechanics
Vol. 726, pp. 312-337 
DOI URL 
Abstract: Numerical simulations of the linear and nonlinear two-dimensional Navier-Stokes equations, and linear stability theory are used to parametrically investigate hypersonic boundary layers over ultrasonic absorptive coatings. The porous coatings consist of a uniform array of rectangular pores (slots) with a range of porosities and pore aspect ratios. For the numerical simulations, temporally (rather than spatially) evolving boundary layers are considered and we provide evidence that this approximation is appropriate for slowly growing second-mode instabilities. We consider coatings operating in the typical regime where the pores are relatively deep and acoustic waves and second-mode instabilities are attenuated by viscous effects inside the pores, as well as regimes with phase cancellation or reinforcement associated with reflection of acoustic waves from the bottom of the pores. These conditions are defined as attenuative and cancellation/reinforcement regimes, respectively. The focus of the present study is on the cases which have not been systematically studied in the past, namely the reinforcement regime (which represents a worst-case scenario, i.e. minimal second-mode damping) and the cancellation regime (which corresponds to the configuration with the most potential improvement). For all but one of the cases considered, the linear simulations show good agreement with the results of linear instability theory that employs an approximate porous-wall boundary condition, and confirm that the porous coating stabilizing performance is directly related to their acoustic scattering performance. A particular case with relatively shallow pores and very high porosity showed the existence of a shorter-wavelength instability that was not initially predicted by theory. Our analysis shows that this new mode is associated with acoustic resonances in the pores and can be more unstable than the second mode. Modifications to the theoretical model are suggested to account for the new mode and to provide estimates of the porous coating parameters that avoid this detrimental instability. Finally, nonlinear simulations confirm the conclusions of the linear analysis; in particular, we did not observe any tripping of the boundary layer by small-scale disturbances associated with individual pores.
BibTeX:
@article{BresInkmanColoniusEtAl2013,
  author = {Brès, G. A. and Inkman, M. and Colonius, T. and Fedorov, A. V.},
  title = {Second-mode attenuation and cancellation by porous coatings in a high-speed boundary layer},
  journal = {Journal of Fluid Mechanics},
  year = {2013},
  volume = {726},
  pages = {312-337},
  url = {http://colonius.caltech.edu/pdfs/BresInkmanColoniusEtAl2013.pdf},
  doi = {https://doi.org/10.1017/jfm.2013.206}
}
Cavalieri, A.V.G., Rodríguez, D., Jordan, P., Colonius, T. and Gervais, Y. Wavepackets in the velocity field of turbulent jets 2013 Journal of Fluid Mechanics
Vol. 730, pp. 559-592 
DOI URL 
Abstract: We study the velocity fields of unforced, high Reynolds number, subsonic jets, issuing from round nozzles with turbulent boundary layers. The objective of the study is to educe wavepackets in such flows and to explore their relationship with the radiated sound. The velocity field is measured using a hot-wire anemometer and a stereoscopic, time-resolved PIV system. The field can be decomposed into frequency and azimuthal Fourier modes. The low-angle sound radiation is measured synchronously with a microphone ring array. Consistent with previous observations, the azimuthal wavenumber spectra of the velocity and acoustic pressure fields are distinct. The velocity spectrum of the initial mixing layer exhibits a peak at azimuthal wavenumbers m ranging from 4 to 11, and the peak is found to scale with the local momentum thickness of the mixing layer. The acoustic pressure field is, on the other hand, predominantly axisymmetric, suggesting an increased relative acoustic efficiency of the axisymmetric mode of the velocity field, a characteristic that can be shown theoretically to be caused by the radial compactness of the sound source. This is confirmed by significant correlations, as high as 10%, between the axisymmetric modes of the velocity and acoustic pressure fields, these values being significantly higher than those reported for two-point flow-acoustic correlations in subsonic jets. The axisymmetric and first helical modes of the velocity field are then compared with solutions of linear parabolized stability equations (PSE) to ascertain if these modes correspond to linear wavepackets. For all but the lowest frequencies close agreement is obtained for the spatial amplification, up to the end of the potential core. The radial shapes of the linear PSE solutions also agree with the experimental results over the same region. The results suggests that, despite the broadband character of the turbulence, the evolution of Strouhal numbers 0.3 <= St <= 0.9 and azimuthal modes 0 and 1 can be modelled as linear wavepackets, and these are associated with the sound radiated to low polar angles.
BibTeX:
@article{CavalieriRodriguezJordanEtAl2013,
  author = {Cavalieri, A. V. G. and Rodríguez, D. and Jordan, P. and Colonius, T. and Gervais, Y.},
  title = {Wavepackets in the velocity field of turbulent jets},
  journal = {Journal of Fluid Mechanics},
  year = {2013},
  volume = {730},
  pages = {559-592},
  url = {http://colonius.caltech.edu/pdfs/CavalieriRodriguezJordanEtAl2013.pdf},
  doi = {https://doi.org/10.1017/jfm.2013.346}
}
Choi, J., Colonius, T. and Williams, D. Dynamics and Energy Extraction of a Surging and Plunging Airfoil at Low Reynolds Number 2013 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition  DOI URL 
BibTeX:
@inproceedings{ChoiColoniusWilliams2013,
  author = {Choi, Jeesoon and Colonius, Tim and Williams, David},
  title = {Dynamics and Energy Extraction of a Surging and Plunging Airfoil at Low Reynolds Number},
  booktitle = {51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2013},
  url = {http://colonius.caltech.edu/pdfs/ChoiColoniusWilliams2013.pdf},
  doi = {https://doi.org/10.2514/6.2013-672}
}
Coralic, V. and Colonius, T. Shock-induced collapse of a bubble inside a deformable vessel 2013 European Journal of Mechanics B-Fluids
Vol. 40, pp. 64-74 
DOI URL 
Abstract: Shockwave lithotripsy repeatedly focuses shockwaves on kidney stones to induce their fracture, partially through cavitation erosion. A typical side effect of the procedure is hemorrhage, which is potentially the result of the growth and collapse of bubbles inside blood vessels. To identify the mechanisms by which shock-induced collapse could lead to the onset of injury, we study an idealized problem involving a preexisting bubble in a deformable vessel. We utilize a high-order accurate, shock- and interface-capturing, finite-volume scheme and simulate the three-dimensional shock-induced collapse of an air bubble immersed in a cylindrical water column which is embedded in a gelatin/water mixture. The mixture is a soft tissue simulant, 10% gelatin by weight, and is modeled by the stiffened gas equation of state. The bubble dynamics of this model configuration are characterized by the collapse of the bubble and its subsequent jetting in the direction of the propagation of the shockwave. The vessel wall, which is defined by the material interface between the water and gelatin/water mixture, is invaginated by the collapse and distended by the impact of the jet. The present results show that the highest measured pressures and deformations occur when the volumetric confinement of the bubble is strongest, the bubble is nearest the vessel wall and/or the angle of incidence of the shockwave reduces the distance between the jet tip and the nearest vessel surface. For a particular case considered, the 40 MPa shockwave utilized in this study to collapse the bubble generated a vessel wall pressure of almost 450 MPa and produced both an invagination and distention of nearly 50% of the initial vessel radius on a O (10) ns timescale. These results are indicative of the significant potential of shock-induced collapse to contribute to the injury of blood vessels in shockwave lithotripsy.
BibTeX:
@article{CoralicColonius2013,
  author = {Coralic, V. and Colonius, T.},
  title = {Shock-induced collapse of a bubble inside a deformable vessel},
  journal = {European Journal of Mechanics B-Fluids},
  year = {2013},
  volume = {40},
  pages = {64-74},
  url = {http://colonius.caltech.edu/pdfs/CoralicColonius2013.pdf},
  doi = {https://doi.org/10.1016/j.euromechflu.2013.01.003}
}
Feldman, Y. and Colonius, T. On a transitional and turbulent natural convection in spherical shells 2013 International Journal of Heat and Mass Transfer
Vol. 64, pp. 514-525 
DOI URL 
Abstract: Laminar and turbulent natural convection inside concentric spherical shells with isothermal cold and hot boundaries is numerically investigated up to Rayleigh number values Ra <= 10(12) and Pr = 0.71. The study utilizes direct numerical simulation (DNS), large eddy simulation (LES) and Reynolds averaged Navier-Stokes (RANS) approaches for investigation of the laminar, transitional and fully developed turbulent flow regimes, respectively. Three-dimensional flow patterns for slightly supercritical oscillatory flow regime inside the shell, with internal/external diameter ratio equal to D-i/D-o = 0.714 are presented and may be potentially useful for verification of the future linear stability analysis results. Particular attention has been given to the complex, fully three-dimensional unsteady flows occurring in narrow shell geometries characterized by 0.85 <= D-i/D-o <= 0.95. For this geometry considerable deviations in predicted heat flux rate through the shell boundaries are observed when compared with existing heat transfer correlations for the entire range of Ra numbers. The deviations tend to increase for transitional and fully turbulent flows. A new correlation for the heat transfer rate is suggested for laminar and transitional flow regimes.
BibTeX:
@article{FeldmanColonius2013,
  author = {Feldman, Y. and Colonius, T.},
  title = {On a transitional and turbulent natural convection in spherical shells},
  journal = {International Journal of Heat and Mass Transfer},
  year = {2013},
  volume = {64},
  pages = {514-525},
  url = {http://colonius.caltech.edu/pdfs/FeldmanColonius2013.pdf},
  doi = {https://doi.org/10.1016/j.ijheatmasstransfer.2013.04.042}
}
Jordan, P. and Colonius, T. Wave Packets and Turbulent Jet Noise 2013 Annual Review of Fluid Mechanics
Vol. 45, pp. 173-195 
DOI URL 
Abstract: Turbulent jet noise is a controversial fluid mechanical puzzle that has amused and bewildered researchers for more than half a century. Whereas numerical simulations are now capable of simultaneously predicting turbulence and its radiated sound, the theoretical framework that would guide noise-control efforts is incomplete. Wave packets are intermittent, advecting disturbances that are correlated over distances far exceeding the integral scales of turbulence. Their signatures are readily distinguished in the vortical, turbulent region; the irrotational, evanescent near field; and the propagating far field. We review evidence of the existence, energetics, dynamics, and acoustic efficiency of wave packets. We highlight how extensive data available from simulations and modern measurement techniques can be used to distill acoustically relevant turbulent motions. The evidence supports theories that seek to represent wave packets as instability waves, or more general modal solutions of the governing equations, and confirms the acoustic importance of these structures in the aft-angle radiation of high subsonic and supersonic jets. The resulting unified view of wave packets provides insights that can help guide control strategies.
BibTeX:
@article{JordanColonius2013,
  author = {Jordan, P. and Colonius, T.},
  title = {Wave Packets and Turbulent Jet Noise},
  journal = {Annual Review of Fluid Mechanics},
  year = {2013},
  volume = {45},
  pages = {173-195},
  url = {http://colonius.caltech.edu/pdfs/JordanColonius2013.pdf},
  doi = {https://doi.org/10.1146/annurev-fluid-011212-140756}
}
Meng, J. and Colonius, T. Droplet Breakup in High-Speed Gas Flows 2013 8th International Conference on Multiphase Flow, Jeju, Korea  URL 
BibTeX:
@inproceedings{MengColonius2013,
  author = {Meng, J.C. and Colonius, T.},
  title = {Droplet Breakup in High-Speed Gas Flows},
  booktitle = {8th International Conference on Multiphase Flow, Jeju, Korea},
  year = {2013},
  url = {http://colonius.caltech.edu/pdfs/MengColonius2013.pdf}
}
Meng, J. and Colonius, T. The Effects of Shock Strength on Droplet Breakup 2013 Proceedings of the 29th International Symposium on Shock Waves, Madison, WI  URL 
BibTeX:
@inproceedings{MengColonius2013a,
  author = {Meng, J.C. and Colonius, T.},
  title = {The Effects of Shock Strength on Droplet Breakup},
  booktitle = {Proceedings of the 29th International Symposium on Shock Waves, Madison, WI},
  year = {2013},
  url = {http://colonius.caltech.edu/pdfs/MengColonius2013a.pdf}
}
Pirozzoli, S. and Colonius, T. Generalized characteristic relaxation boundary conditions for unsteady compressible flow simulations 2013 Journal of Computational Physics
Vol. 248, pp. 109-126 
DOI URL 
Abstract: We develop numerical boundary conditions for the compressible Navier-Stokes equations based on a generalized relaxation approach (GRCBC), which hinges on locally one-dimensional characteristic projection at the computational boundaries, supplemented with available information from the flow exterior. The basic idea is to estimate the amplitude of incoming characteristic waves through first-order one-sided finite-difference approximations which involve the value of the reference flow state at the first exterior ( ghost) point. Unlike other characteristic-based relaxation methods, the present one requires minimal user-supplied input, including the reference flow state, which may be totally or partially known, and in general may vary both in space and time. Furthermore, it can be applied to any type of computational boundary, either inflow or outflow, either subsonic or supersonic. The method is theoretically predicted to convey reduced reflection of waves at computational boundaries compared to other ones, and to have better properties of frequency response to injected disturbances. Numerical tests confirm the improvement of the nonreflecting performance, and demonstrate high degree of flexibility, also for problems with non-trivial far-field boundary conditions (e.g. flows in rotating reference frames) and for the artificial stimulation of subsonic turbulent boundary layers.
BibTeX:
@article{PirozzoliColonius2013,
  author = {Pirozzoli, S. and Colonius, T.},
  title = {Generalized characteristic relaxation boundary conditions for unsteady compressible flow simulations},
  journal = {Journal of Computational Physics},
  year = {2013},
  volume = {248},
  pages = {109-126},
  url = {http://colonius.caltech.edu/pdfs/PirozzoliColonius2013.pdf},
  doi = {https://doi.org/10.1016/j.jcp.2013.04.021}
}
Rodríguez, D., Sinha, A., Brès, G.A. and Colonius, T. Inlet conditions for wave packet models in turbulent jets based on eigenmode decomposition of large eddy simulation data 2013 Physics of Fluids
Vol. 25(10) 
DOI URL 
Abstract: This paper makes contributions towards reduced-order models of wave packets in supersonic, turbulent jets. Wave packets are large-scale turbulent structures that are correlated and advected over distances that are large compared to the integral scales of turbulence, i.e., many jet diameters at the lowest frequencies. They are thought to be responsible for the peak noise radiated at shallow angles to the jet axis. Linear wave packet models based on the Parabolized Stability Equations (PSE) have been shown in the past to be in excellent agreement with statistical structures educed from experimental pressure and velocity data in subsonic jets. Here, we extend these models to supersonic jets and validate them using a Large Eddy Simulation (LES) database for an isothermal and amoderately heated Mach 1.5 turbulent jets. For supersonic jets, inlet conditions for PSE models are ambiguous, as a parallel flow stability analysis shows several unstable modes at the inlet cross section. We develop a bi-orthogonal decomposition and project the LES data onto the relevant families of instability waves. These serve as inlet conditions, including the amplitude and shape functions, for PSE solutions which are then favorably compared to the near-field pressure fields educed from LES.
BibTeX:
@article{RodriguezSinhaBresEtAl2013,
  author = {Rodríguez, D. and Sinha, A. and Brès, G. A. and Colonius, T.},
  title = {Inlet conditions for wave packet models in turbulent jets based on eigenmode decomposition of large eddy simulation data},
  journal = {Physics of Fluids},
  year = {2013},
  volume = {25},
  number = {10},
  url = {http://colonius.caltech.edu/pdfs/RodriguezSinhaBresEtAl2013.pdf},
  doi = {https://doi.org/10.1063/1.4824479}
}
Rodr\iguez, D., Cavalieri, A., Colonius, T. and Jordan, P. Wavepacket eduction in turbulent jets based on eigenmode decomposition of PIV data 2013 19th AIAA/CEAS Aeroacoustics Conference  DOI URL 
BibTeX:
@inproceedings{RodriguezCavalieriColoniusEtAl2013,
  author = {Rodr\iguez, Daniel and Cavalieri, André and Colonius, Tim and Jordan, Peter},
  title = {Wavepacket eduction in turbulent jets based on eigenmode decomposition of PIV data},
  booktitle = {19th AIAA/CEAS Aeroacoustics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2013},
  url = {http://colonius.caltech.edu/pdfs/RodriguezCavalieriColoniusEtAl2013.pdf},
  doi = {https://doi.org/10.2514/6.2013-2084}
}
Rodr\iguez, D., Sinha, A., Brès, G. and Colonius, T. Acoustic field associated with parabolized stability equation models in turbulent jets 2013 19th AIAA/CEAS Aeroacoustics Conference  DOI URL 
BibTeX:
@inproceedings{RodriguezSinhaBresEtAl2013a,
  author = {Rodr\iguez, Daniel and Sinha, Aniruddha and Brès, Guillaume and Colonius, Tim},
  title = {Acoustic field associated with parabolized stability equation models in turbulent jets},
  booktitle = {19th AIAA/CEAS Aeroacoustics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2013},
  url = {http://colonius.caltech.edu/pdfs/RodriguezSinhaBresEtAl2013a.pdf},
  doi = {https://doi.org/10.2514/6.2013-2279}
}
Sinha, A., Schlinker, R., Simonich, J., Reba, R. and Colonius, T. Toward Active Control of Noise from Hot Supersonic Jets 2013 19th AIAA/CEAS Aeroacoustics Conference  DOI URL 
BibTeX:
@inproceedings{SinhaSchlinkerSimonichEtAl2013,
  author = {Sinha, Aniruddha and Schlinker, Robert and Simonich, John and Reba, Ramons and Colonius, Tim},
  title = {Toward Active Control of Noise from Hot Supersonic Jets},
  booktitle = {19th AIAA/CEAS Aeroacoustics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2013},
  url = {http://colonius.caltech.edu/pdfs/SinhaSchlinkerSimonichEtAl2013.pdf},
  doi = {https://doi.org/10.2514/6.2013-2234}
}
Towne, A. and Colonius, T. Improved Parabolization of the Euler Equations 2013 19th AIAA/CEAS Aeroacoustics Conference  DOI URL 
BibTeX:
@inproceedings{TowneColonius2013,
  author = {Towne, Aaron and Colonius, Tim},
  title = {Improved Parabolization of the Euler Equations},
  booktitle = {19th AIAA/CEAS Aeroacoustics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2013},
  url = {http://colonius.caltech.edu/pdfs/TowneColonius2013.pdf},
  doi = {https://doi.org/10.2514/6.2013-2171}
}
Cavalieri, A.V.G., Jordan, P., Colonius, T. and Gervais, Y. Axisymmetric superdirectivity in subsonic jets 2012 Journal of Fluid Mechanics
Vol. 704, pp. 388-420 
DOI URL 
Abstract: We present experimental results for the acoustic field of jets with Mach numbers between 0.35 and 0.6. An azimuthal ring array of six microphones, whose polar angle, theta, was progressively varied, allows the decomposition of the acoustic pressure into azimuthal Fourier modes. In agreement with past observations, the sound field for low polar angles (measured with respect to the jet axis) is found to be dominated by the axisymmetric mode, particularly at the peak Strouhal number. The axisymmetric mode of the acoustic field can be clearly associated with an axially non-compact source, in the form of a wavepacket: the sound pressure level for peak frequencies is found be superdirective for all Mach numbers considered, with exponential decay as a function of (1 - M-c cos theta)(2), where M-c is the Mach number based on the phase velocity U-c of the convected wave. While the mode m = 1 spectrum scales with Strouhal number, suggesting that its energy content is associated with turbulence scales, the axisymmetric mode scales with Helmholtz number - the ratio between source length scale and acoustic wavelength. The axisymmetric radiation has a stronger velocity dependence than the higher-order azimuthal modes, again in agreement with predictions of wavepacket models. We estimate the axial extent of the source of the axisymmetric component of the sound field to be of the order of six to eight jet diameters. This estimate is obtained in two different ways, using, respectively, the directivity shape and the velocity exponent of the sound radiation. The analysis furthermore shows that compressibility plays a significant role in the wavepacket dynamics, even at this low Mach number. Velocity fluctuations on the jet centreline are reduced as the Mach number is increased, an effect that must be accounted for in order to obtain a correct estimation of the velocity dependence of sound radiation. Finally, the higher-order azimuthal modes of the sound field are considered, and a model for the low-angle sound radiation by helical wavepackets is developed. The measured sound for azimuthal modes 1 and 2 at low Strouhal numbers is seen to correspond closely to the predicted directivity shapes.
BibTeX:
@article{CavalieriJordanColoniusEtAl2012,
  author = {Cavalieri, A. V. G. and Jordan, P. and Colonius, T. and Gervais, Y.},
  title = {Axisymmetric superdirectivity in subsonic jets},
  journal = {Journal of Fluid Mechanics},
  year = {2012},
  volume = {704},
  pages = {388-420},
  url = {http://colonius.caltech.edu/pdfs/CavalieriJordanColoniusEtAl2012.pdf},
  doi = {https://doi.org/10.1017/jfm.2012.247}
}
Cavalieri André, C., Rodr\iguez, D., Jordan, P., Colonius, T. and Gervais, Y. Wavepackets in the velocity field of turbulent jets 2012 18th AIAA/CEAS Aeroacoustics Conference (33rd AIAA Aeroacoustics Conference)  DOI URL 
BibTeX:
@inproceedings{CavalieriRodriguezJordanEtAl2012,
  author = {Cavalieri, André, Cavalieri and Rodr\iguez, Daniel and Jordan, Peter and Colonius, Tim and Gervais, Yves},
  title = {Wavepackets in the velocity field of turbulent jets},
  booktitle = {18th AIAA/CEAS Aeroacoustics Conference (33rd AIAA Aeroacoustics Conference)},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2012},
  url = {http://colonius.caltech.edu/pdfs/CavalieriRodriguezJordanEtAl2012.pdf},
  doi = {https://doi.org/10.2514/6.2012-2115}
}
Cavalieri André, C., Violato, D., Rodr\iguez, D., Jordan, P., Scarano, F., Colonius, T. and Gervais, Y. Low-speed jet dynamics and sound radiation 2012 18th AIAA/CEAS Aeroacoustics Conference (33rd AIAA Aeroacoustics Conference)  DOI URL 
BibTeX:
@inproceedings{CavalieriViolatoRodriguezEtAl2012,
  author = {Cavalieri, André, Cavalieri and Violato, Daniele and Rodr\iguez, Daniel and Jordan, Peter and Scarano, Fulvio and Colonius, Tim and Gervais, Yves},
  title = {Low-speed jet dynamics and sound radiation},
  booktitle = {18th AIAA/CEAS Aeroacoustics Conference (33rd AIAA Aeroacoustics Conference)},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2012},
  url = {http://colonius.caltech.edu/pdfs/CavalieriViolatoRodriguezEtAl2012.pdf},
  doi = {https://doi.org/10.2514/6.2012-2080}
}
Colonius, T. and Fuster, D. Investigation of a New Model for Bubbly Cavitating Flow 2012 CAV2012: Eighth International Symposium on Cavitation, Singapore  URL 
BibTeX:
@inproceedings{ColoniusFuster2012,
  author = {Colonius, T. and Fuster, D.},
  title = {Investigation of a New Model for Bubbly Cavitating Flow},
  booktitle = {CAV2012: Eighth International Symposium on Cavitation, Singapore},
  year = {2012},
  url = {http://colonius.caltech.edu/pdfs/ColoniusFuster2012.pdf}
}
Feldman, Y., Colonius, T., Pauken, M.T., Hall, J.L. and Jones, J.A. Simulation and Cryogenic Experiments of Natural Convection for the Titan Montgolfiere 2012 AIAA Journal
Vol. 50(11), pp. 2483-2491 
DOI URL 
Abstract: Natural convection in a spherical geometry is considered for prediction of the buoyancy of single- and double-walled balloons in a cryogenic environment such as Titan's atmosphere. The steady-state flow characteristics obtained by solving the Reynolds-averaged Navier-Stokes equations with a standard turbulence model are used to determine the net buoyancy as a function of heat input. Thermal radiation effects are shown to have a minor impact on the buoyancy, as would he expected at cryogenic conditions. The predicted buoyancy and temperature fields compare favorably with experiments preformed on a 1-m-diameter Montgolfiere prototype in a cryogenic facility. In addition, both numerical and experimental results were compared with correlations for the heat transfer coefficients for free convection internal and external to the balloon as well as in the concentric gap of the double-walled balloons. Finally, scaling issues related to inferring the performance of the full-scale Montgolfiere from the model-scale results are examined.
BibTeX:
@article{FeldmanColoniusPaukenEtAl2012,
  author = {Feldman, Y. and Colonius, T. and Pauken, M. T. and Hall, J. L. and Jones, J. A.},
  title = {Simulation and Cryogenic Experiments of Natural Convection for the Titan Montgolfiere},
  journal = {AIAA Journal},
  year = {2012},
  volume = {50},
  number = {11},
  pages = {2483-2491},
  url = {http://colonius.caltech.edu/pdfs/FeldmanColoniusPaukenEtAl2012.pdf},
  doi = {https://doi.org/10.2514/1.J051672}
}
Franck, J.A. and Colonius, T. Effects of Actuation Frequency on Flow Control Applied to a Wall-Mounted Hump 2012 AIAA Journal
Vol. 50(7), pp. 1631-1634 
DOI URL 
BibTeX:
@article{FranckColonius2012,
  author = {Franck, J. A. and Colonius, T.},
  title = {Effects of Actuation Frequency on Flow Control Applied to a Wall-Mounted Hump},
  journal = {AIAA Journal},
  year = {2012},
  volume = {50},
  number = {7},
  pages = {1631-1634},
  url = {http://colonius.caltech.edu/pdfs/FranckColonius2012.pdf},
  doi = {https://doi.org/10.2514/1.J051183}
}
Hagstrom, T., Appelö, D., Colonius, T., Inkman, M. and Jang, C.Y. Simulation of compressible flows using Hermite methods 2012
Vol. 131(4)Acoustic 2012, Hong Kong, pp. 3429-3429 
DOI  
BibTeX:
@inproceedings{HagstromAppeloeColoniusEtAl2012,
  author = {Hagstrom, Thomas and Appelö, Daniel and Colonius, Tim and Inkman, Matthew and Jang, Chang Youn},
  title = {Simulation of compressible flows using Hermite methods},
  booktitle = {Acoustic 2012, Hong Kong},
  year = {2012},
  volume = {131},
  number = {4},
  pages = {3429-3429},
  doi = {https://doi.org/10.1121/1.4708863}
}
Jang, C.Y., Appelö, D., Colonius, T., Hagstrom, T. and Inkman, M. An Analysis of Dispersion and Dissipation Properties of Hermite Methods and its Application to Direct Numerical Simulation of Jet Noise 2012 18th AIAA/CEAS Aeroacoustics Conference (33rd AIAA Aeroacoustics Conference)  DOI URL 
BibTeX:
@inproceedings{JangAppeloeColoniusEtAl2012,
  author = {Jang, Chang Young and Appelö, Daniel and Colonius, Tim and Hagstrom, Thomas and Inkman, Matthew},
  title = {An Analysis of Dispersion and Dissipation Properties of Hermite Methods and its Application to Direct Numerical Simulation of Jet Noise},
  booktitle = {18th AIAA/CEAS Aeroacoustics Conference (33rd AIAA Aeroacoustics Conference)},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2012},
  url = {http://colonius.caltech.edu/pdfs/JangAppeloeColoniusEtAl2012.pdf},
  doi = {https://doi.org/10.2514/6.2012-2240}
}
Li, X.B., Hunt, M.L. and Colonius, T. A contact model for normal immersed collisions between a particle and a wall 2012 Journal of Fluid Mechanics
Vol. 691, pp. 123-145 
DOI URL 
Abstract: The incompressible Navier-Stokes equations are solved numerically to predict the coupled motion of a falling particle and the surrounding fluid as the particle impacts and rebounds from a planar wall. The method is validated by comparing the numerical simulations of a settling sphere with experimental measurements of the sphere trajectory and the accompanying flow field. The normal collision process is then studied for a range of impact Stokes numbers. A contact model of the liquid solid interaction and elastic effect is developed that incorporates the elasticity of the solids to permit the rebound trajectory to be simulated accurately. The contact model is applied when the particle is sufficiently close to the wall that it becomes difficult to resolve the thin lubrication layer. The model is calibrated with new measurements of the particle trajectories and reproduces the observed coefficient of restitution over a range of impact Stokes numbers from 1 to 1000.
BibTeX:
@article{LiHuntColonius2012,
  author = {Li, X. B. and Hunt, M. L. and Colonius, T.},
  title = {A contact model for normal immersed collisions between a particle and a wall},
  journal = {Journal of Fluid Mechanics},
  year = {2012},
  volume = {691},
  pages = {123-145},
  url = {http://colonius.caltech.edu/pdfs/LiHuntColonius2012.pdf},
  doi = {https://doi.org/10.1017/jfm.2011.461}
}
Regele, J., Rabinovitch, J., Colonius, T. and Blanquart, G. Numerical Modeling and Analysis of Early Shock Wave Interactions with a Dense Particle Cloud 2012 42nd AIAA Fluid Dynamics Conference and Exhibit  DOI URL 
BibTeX:
@inproceedings{RegeleRabinovitchColoniusEtAl2012,
  author = {Regele, Jonathan and Rabinovitch, Jason and Colonius, Tim and Blanquart, Guillaume},
  title = {Numerical Modeling and Analysis of Early Shock Wave Interactions with a Dense Particle Cloud},
  booktitle = {42nd AIAA Fluid Dynamics Conference and Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2012},
  url = {http://colonius.caltech.edu/pdfs/RegeleRabinovitchColoniusEtAl2012.pdf},
  doi = {https://doi.org/10.2514/6.2012-3161}
}
Rodr\iguez, D., Sinha, A., Brès, G. and Colonius, T. Parabolized stability equation models in turbulent supersonic jets 2012 18th AIAA/CEAS Aeroacoustics Conference (33rd AIAA Aeroacoustics Conference)  DOI URL 
BibTeX:
@inproceedings{RodriguezSinhaBresEtAl2012,
  author = {Rodr\iguez, Daniel and Sinha, Aniruddha and Brès, Guillaume and Colonius, Tim},
  title = {Parabolized stability equation models in turbulent supersonic jets},
  booktitle = {18th AIAA/CEAS Aeroacoustics Conference (33rd AIAA Aeroacoustics Conference)},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2012},
  url = {http://colonius.caltech.edu/pdfs/RodriguezSinhaBresEtAl2012.pdf},
  doi = {https://doi.org/10.2514/6.2012-2117}
}
Sanada, T., Ando, K. and Colonius, T. Effects of Target Compliance on a High-Speed Droplet Impact 2012 Ultra Clean Processing of Semiconductor Surfaces X
Vol. 187, pp. 137-140 
DOI URL 
Abstract: High speed spray cleaning which utilize droplets impact has been used for removing contaminants from wafer surface. When a droplet impacts a solid surface at high speed, the contact periphery expands very quickly and liquid compressibility plays an important role in the initial dynamics and the formation of lateral jets. Impact results in high pressures that can clean or damage the surface. In this study, we numerically investigated a high speed droplet impacts on a solid wall. In order to compare the available theory and experiments, 1 D, 2D and axisymmetric solutions are obtained. The generated pressures, shock speeds, and the lateral jetting mechanism are investigated; especially the effect of target compliance is focused.
BibTeX:
@article{SanadaAndoColonius2012,
  author = {Sanada, T. and Ando, K. and Colonius, T.},
  title = {Effects of Target Compliance on a High-Speed Droplet Impact},
  journal = {Ultra Clean Processing of Semiconductor Surfaces X},
  year = {2012},
  volume = {187},
  pages = {137-140},
  url = {http://colonius.caltech.edu/pdfs/SanadaAndoColonius2012.pdf},
  doi = {https://doi.org/10.4028/www.scientific.net/SSP.187.137}
}
Sinha, A., Alkandry, H., Kearney-Fischer, M., Samimy, M. and Colonius, T. The impulse response of a high-speed jet forced with localized arc filament plasma actuators 2012 Physics of Fluids
Vol. 24(12) 
DOI URL 
Abstract: We present experimental and theoretical analyses of the response of high-speed, high-Reynolds-number, round jets to impulsive forcing with arc-filament-plasma actuators. The impulse response is obtained with forcing Strouhal numbers, based on the nozzle exit diameter and exit center line velocity, less than 0.1. The resulting phase-averaged near-field pressure signature displays a compact wave with a positive peak preceding a negative one, indicative of a large scale structure in the shear layer of the jet. Scaling laws derived by operating the jet at four subsonic Mach numbers are used to distinguish this hydrodynamic component of the phase-averaged jet response from the direct actuator noise. As the forcing frequency increases, the compact waves in the near-field pressure signal overlap each other, indicating interaction of the growing seeded structures. For this regime, the phase-averaged response is approximately replicated by linear superposition of the impulse response, thereby demonstrating the quasi-linearity of structure interaction. A novel application of linear parabolized stability theory yields a successful model of the impulse response.
BibTeX:
@article{SinhaAlkandryKearney-FischerEtAl2012,
  author = {Sinha, A. and Alkandry, H. and Kearney-Fischer, M. and Samimy, M. and Colonius, T.},
  title = {The impulse response of a high-speed jet forced with localized arc filament plasma actuators},
  journal = {Physics of Fluids},
  year = {2012},
  volume = {24},
  number = {12},
  url = {http://colonius.caltech.edu/pdfs/SinhaAlkandryKearney-FischerEtAl2012.pdf},
  doi = {https://doi.org/10.1063/1.4772191}
}
Ando, K., Colonius, T. and Brennen, C.E. Numerical simulation of shock propagation in a polydisperse bubbly liquid 2011 International Journal of Multiphase Flow
Vol. 37(6), pp. 596-608 
DOI URL 
Abstract: The effect of distributed bubble nuclei sizes on shock propagation in a bubbly liquid is numerically investigated. An ensemble-averaged technique is employed to derive the statistically averaged conservation laws for polydisperse bubbly flows. A finite-volume method is developed to solve the continuum bubbly flow equations coupled to a single-bubble-dynamic equation that incorporates the effects of heat transfer, liquid viscosity and compressibility. The one-dimensional shock computations reveal that the distribution of equilibrium bubble sizes leads to an apparent damping of the averaged shock dynamics due to phase cancellations in oscillations of the different-sized bubbles. If the distribution is sufficiently broad, the phase cancellation effect can dominate over the single-bubble-dynamic dissipation and the averaged shock profile is smoothed out.
BibTeX:
@article{AndoColoniusBrennen2011,
  author = {Ando, K. and Colonius, T. and Brennen, C. E.},
  title = {Numerical simulation of shock propagation in a polydisperse bubbly liquid},
  journal = {International Journal of Multiphase Flow},
  year = {2011},
  volume = {37},
  number = {6},
  pages = {596-608},
  url = {http://colonius.caltech.edu/pdfs/AndoColoniusBrennen2011.pdf},
  doi = {https://doi.org/10.1016/j.ijmultiphaseflow.2011.03.007}
}
Ando, K., Sanada, T., Inaba, K., Damazo, J.S., Shepherd, J.E., Colonius, T. and Brennen, C.E. Shock propagation through a bubbly liquid in a deformable tube 2011 Journal of Fluid Mechanics
Vol. 671, pp. 339-363 
DOI URL 
Abstract: Shock propagation through a bubbly liquid contained in a deformable tube is considered. Quasi-one-dimensional mixture-averaged flow equations that include fluid-structure interaction are formulated. The steady shock relations are derived and the nonlinear effect due to the gas-phase compressibility is examined. Experiments are conducted in which a free-falling steel projectile impacts the top of an air/water mixture in a polycarbonate tube, and stress waves in the tube material and pressure on the tube wall are measured. The experimental data indicate that the linear theory is incapable of properly predicting the propagation speeds of finite-amplitude waves in a mixture-filled tube; the shock theory is found to more accurately estimate the measured wave speeds.
BibTeX:
@article{AndoSanadaInabaEtAl2011,
  author = {Ando, K. and Sanada, T. and Inaba, K. and Damazo, J. S. and Shepherd, J. E. and Colonius, T. and Brennen, C. E.},
  title = {Shock propagation through a bubbly liquid in a deformable tube},
  journal = {Journal of Fluid Mechanics},
  year = {2011},
  volume = {671},
  pages = {339-363},
  url = {http://colonius.caltech.edu/pdfs/AndoSanadaInabaEtAl2011.pdf},
  doi = {https://doi.org/10.1017/S0022112010005707}
}
Appelö, D., Inkman, M., Hagstrom, T. and Colonius, T. Hermite Methods for Aeroacoustics: Recent Progress 2011 17th AIAA/CEAS Aeroacoustics Conference (32nd AIAA Aeroacoustics Conference)  DOI URL 
BibTeX:
@inproceedings{AppeloeInkmanHagstromEtAl2011,
  author = {Appelö, Daniel and Inkman, Matthew and Hagstrom, Thomas and Colonius, Tim},
  title = {Hermite Methods for Aeroacoustics: Recent Progress},
  booktitle = {17th AIAA/CEAS Aeroacoustics Conference (32nd AIAA Aeroacoustics Conference)},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2011},
  url = {http://colonius.caltech.edu/pdfs/AppeloeInkmanHagstromEtAl2011.pdf},
  doi = {https://doi.org/10.2514/6.2011-2757}
}
Brès, G., Fares, E., Williams, D. and Colonius, T. Numerical Simulations of the Transient Flow Response of a 3D, Low-Aspect-Ratio Wing to Pulsed Actuation 2011 41st AIAA Fluid Dynamics Conference and Exhibit  DOI URL 
BibTeX:
@inproceedings{BresFaresWilliamsEtAl2011,
  author = {Brès, Guillaume and Fares, Ehab and Williams, David and Colonius, Tim},
  title = {Numerical Simulations of the Transient Flow Response of a 3D, Low-Aspect-Ratio Wing to Pulsed Actuation},
  booktitle = {41st AIAA Fluid Dynamics Conference and Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2011},
  url = {http://colonius.caltech.edu/pdfs/BresFaresWilliamsEtAl2011.pdf},
  doi = {https://doi.org/10.2514/6.2011-3440}
}
Cavalieri, A., Jordan, P., Colonius, T. and Gervais, Y. Axisymmetric superdirectivity in subsonic jets 2011 17th AIAA/CEAS Aeroacoustics Conference (32nd AIAA Aeroacoustics Conference)  DOI URL 
BibTeX:
@inproceedings{CavalieriJordanColoniusEtAl2011,
  author = {Cavalieri, André and Jordan, Peter and Colonius, Tim and Gervais, Yves},
  title = {Axisymmetric superdirectivity in subsonic jets},
  booktitle = {17th AIAA/CEAS Aeroacoustics Conference (32nd AIAA Aeroacoustics Conference)},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2011},
  url = {http://colonius.caltech.edu/pdfs/CavalieriJordanColoniusEtAl2011.pdf},
  doi = {https://doi.org/10.2514/6.2011-2743}
}
Colonius, T. and Williams, D.R. Control of vortex shedding on two- and three-dimensional aerofoils 2011 Philosophical Transactions of the Royal Society a-Mathematical Physical and Engineering Sciences
Vol. 369(1940), pp. 1525-1539 
DOI URL 
Abstract: We review and expand on the control of separated flows over flat plates and aerofoils at low Reynolds numbers associated with micro air vehicles. Experimental observations of the steady-state and transient lift response to actuation, and its dependence on the actuator, aerofoil geometry and flow conditions, are discussed and an attempt is made to unify them in terms of their excitation of periodic and transient vortex shedding. We also examine strategies for closed-loop flow and flight control using actuation of leading-edge vortices.
BibTeX:
@article{ColoniusWilliams2011,
  author = {Colonius, T. and Williams, D. R.},
  title = {Control of vortex shedding on two- and three-dimensional aerofoils},
  journal = {Philosophical Transactions of the Royal Society a-Mathematical Physical and Engineering Sciences},
  year = {2011},
  volume = {369},
  number = {1940},
  pages = {1525-1539},
  url = {http://colonius.caltech.edu/pdfs/ColoniusWilliams2011.pdf},
  doi = {https://doi.org/10.1098/rsta.2010.0355}
}
Coralic, V. and Colonius, T. Numerical simulation of bubble dynamics in deformable vessels 2011 161st Meeting of the Acoustical Society of America  DOI  
BibTeX:
@inproceedings{CoralicColonius2011,
  author = {Coralic, Vedran and Colonius, Tim},
  title = {Numerical simulation of bubble dynamics in deformable vessels},
  booktitle = {161st Meeting of the Acoustical Society of America},
  year = {2011},
  doi = {https://doi.org/10.1121/1.3587690}
}
Fedorov, A., Brès, G., Inkman, M. and Colonius, T. Instability of Hypersonic Boundary Layer on a Wall with Resonating Micro-Cavities 2011 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition  DOI URL 
BibTeX:
@inproceedings{FedorovBresInkmanEtAl2011,
  author = {Fedorov, Alexander and Brès, Guillaume and Inkman, Matthew and Colonius, Tim},
  title = {Instability of Hypersonic Boundary Layer on a Wall with Resonating Micro-Cavities},
  booktitle = {49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2011},
  url = {http://colonius.caltech.edu/pdfs/FedorovBresInkmanEtAl2011.pdf},
  doi = {https://doi.org/10.2514/6.2011-373}
}
Feldman, Y., Samanta, A., Colonius, T., Pauken, M., Hall, J. and Jones, J. Numerical and Experimental Modeling of Natural Convection for a Cryogenic Prototype of a Titan Montgolfiere 2011 11th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference  DOI URL 
BibTeX:
@inproceedings{FeldmanSamantaColoniusEtAl2011,
  author = {Feldman, Yuri and Samanta, Arnab and Colonius, Tim and Pauken, Mike and Hall, Jeffery and Jones, Jack},
  title = {Numerical and Experimental Modeling of Natural Convection for a Cryogenic Prototype of a Titan Montgolfiere},
  booktitle = {11th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2011},
  url = {http://colonius.caltech.edu/pdfs/FeldmanSamantaColoniusEtAl2011.pdf},
  doi = {https://doi.org/10.2514/6.2011-6869}
}
Fuster, D. and Colonius, T. Modelling bubble clusters in compressible liquids 2011 Journal of Fluid Mechanics
Vol. 688, pp. 352-389 
DOI URL 
Abstract: We present a new model for bubbly cavitating flows. Based on volume-averaged equations, a subgrid model is added to account for a bubble, or multiple bubbles, within each computational cell. The model converges to the solution of ensemble-averaged bubbly flow equations for weak oscillations and monodisperse systems. In the other extreme, it also converges to the theoretical solution for a single oscillating bubble, and captures the bubble radius evolution and the pressure disturbance induced in the liquid. A substantial saving of computational time is achieved compared to ensemble-averaged models for polydisperse mixtures.
BibTeX:
@article{FusterColonius2011,
  author = {Fuster, D. and Colonius, T.},
  title = {Modelling bubble clusters in compressible liquids},
  journal = {Journal of Fluid Mechanics},
  year = {2011},
  volume = {688},
  pages = {352-389},
  url = {http://colonius.caltech.edu/pdfs/FusterColonius2011.pdf},
  doi = {https://doi.org/10.1017/jfm.2011.380}
}
Guðmundsson, K. and Colonius, T. Instability wave models for the near-field fluctuations of turbulent jets 2011 Journal of Fluid Mechanics
Vol. 689, pp. 97-128 
DOI URL 
Abstract: Previous work has shown that aspects of the evolution of large-scale structures, particularly in forced and transitional mixing layers and jets, can be described by linear and nonlinear stability theories. However, questions persist as to the choice of the basic (steady) flow field to perturb, and the extent to which disturbances in natural (unforced), initially turbulent jets may be modelled with the theory. For unforced jets, identification is made difficult by the lack of a phase reference that would permit a portion of the signal associated with the instability wave to be isolated from other, uncorrelated fluctuations. In this paper, we investigate the extent to which pressure and velocity fluctuations in subsonic, turbulent round jets can be described as linear perturbations to the mean flow field. The disturbances are expanded about the experimentally measured jet mean flow field, and evolved using linear parabolized stability equations (PSE) that account, in an approximate way, for the weakly non-parallel jet mean flow field. We utilize data from an extensive microphone array that measures pressure fluctuations just outside the jet shear layer to show that, up to an unknown initial disturbance spectrum, the phase, wavelength, and amplitude envelope of convecting wavepackets agree well with PSE solutions at frequencies and azimuthal wavenumbers that can be accurately measured with the array. We next apply the proper orthogonal decomposition to near-field velocity fluctuations measured with particle image velocimetry, and show that the structure of the most energetic modes is also similar to eigenfunctions from the linear theory. Importantly, the amplitudes of the modes inferred from the velocity fluctuations are in reasonable agreement with those identified from the microphone array. The results therefore suggest that, to predict, with reasonable accuracy, the evolution of the largest-scale structures that comprise the most energetic portion of the turbulent spectrum of natural jets, nonlinear effects need only be indirectly accounted for by considering perturbations to the mean turbulent flow field, while neglecting any non-zero frequency disturbance interactions.
BibTeX:
@article{GuhmundssonColonius2011,
  author = {Guðmundsson, K. and Colonius, T.},
  title = {Instability wave models for the near-field fluctuations of turbulent jets},
  journal = {Journal of Fluid Mechanics},
  year = {2011},
  volume = {689},
  pages = {97-128},
  url = {http://colonius.caltech.edu/pdfs/GuhmundssonColonius2011.pdf},
  doi = {https://doi.org/10.1017/jfm.2011.401}
}
Hartmann, D. and Colonius, T. A projection method for multiphase flows 2011 20th AIAA Computational Fluid Dynamics Conference  DOI URL 
BibTeX:
@inproceedings{HartmannColonius2011,
  author = {Hartmann, Daniel and Colonius, Tim},
  title = {A projection method for multiphase flows},
  booktitle = {20th AIAA Computational Fluid Dynamics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2011},
  url = {http://colonius.caltech.edu/pdfs/HartmannColonius2011.pdf},
  doi = {https://doi.org/10.2514/6.2011-3831}
}
Joe, W., Colonius, T. and MacMynowski, D. Feedback control of vortex shedding from an inclined flat plate 2011 Theoretical and Computational Fluid Dynamics
Vol. 25(1-4), pp. 221-232 
DOI URL 
Abstract: Open- and closed-loop control of vortex shedding in two-dimensional flow over a flat plate at high angle of attack is numerically investigated at a Reynolds number of 300. Unsteady actuation is modeled as a body force near the leading or trailing edge and is directed either upstream or downstream. For moderate angles of attack, sinusoidal forcing at the natural shedding frequency results in phase locking, with a periodic variation of lift at the same frequency, leading to higher unsteady lift than the natural shedding. However, at sufficiently high angles of attack, a subharmonic of the forcing frequency is also excited and the average lift over the forcing period varies from cycle-to-cycle in a complex manner. It is observed that the periods with the highest averaged lift are associated with particular phase differences between the forcing and the lift, but that this highest-lift shedding cycle is not always stably maintained with open-loop forcing. We design a feedback algorithm to lock the forcing with the phase shift associated with the highest period-averaged lift. It is shown that the compensator results in a stable phase-locked limit cycle for a broader range of forcing frequencies than the open-loop control, and that it is able to stabilize otherwise unstable high-lift limit cycles that cannot be obtained with open-loop control. For example, at an angle of attack of 40A degrees, the feedback controller can increase the averaged magnitude of force on the plate by 76% and increase the averaged lift coefficient from 1.33 to 2.43.
BibTeX:
@article{JoeColoniusMacMynowski2011,
  author = {Joe, W. and Colonius, T. and MacMynowski, D.},
  title = {Feedback control of vortex shedding from an inclined flat plate},
  journal = {Theoretical and Computational Fluid Dynamics},
  year = {2011},
  volume = {25},
  number = {1-4},
  pages = {221-232},
  url = {http://colonius.caltech.edu/pdfs/JoeColoniusMacMynowski2011.pdf},
  doi = {https://doi.org/10.1007/s00162-010-0204-8}
}
Kerstens, W., Pfeiffer, J., Williams, D., King, R. and Colonius, T. Closed-Loop Control of Lift for Longitudinal Gust Suppression at Low Reynolds Numbers 2011 AIAA Journal
Vol. 49(8), pp. 1721-1728 
DOI URL 
Abstract: Experiments are conducted to investigate the ability of variable-pressure pulsed-blowing actuation to maintain a constant lift force on a low-aspect-ratio semicircular wing in a longitudinally gusting flow. Dynamic models of the lift response to actuation and the lift response to longitudinal gusting are obtained through modern system identification methods. Robust closed-loop controllers are synthesized using a mixed-sensitivity loop-shaping approach. An additional feedforward disturbance compensator is designed based on a model of the unsteady aerodynamics. The controllers show suppression of lift fluctuations at low gust frequencies, f < 0.8 Hz (reduced frequency, k < 0.09). At higher frequencies, the control performance degrades due to limitations related to the time for a disturbance, created by the actuators, to convect over the wing and establish the flowfield that leads to enhanced lift on the wing.
BibTeX:
@article{KerstensPfeifferWilliamsEtAl2011,
  author = {Kerstens, W. and Pfeiffer, J. and Williams, D. and King, R. and Colonius, T.},
  title = {Closed-Loop Control of Lift for Longitudinal Gust Suppression at Low Reynolds Numbers},
  journal = {AIAA Journal},
  year = {2011},
  volume = {49},
  number = {8},
  pages = {1721-1728},
  url = {http://colonius.caltech.edu/pdfs/KerstensPfeifferWilliamsEtAl2011.pdf},
  doi = {https://doi.org/10.2514/1.J050954}
}
Olsman, W.F.J. and Colonius, T. Numerical Simulation of Flow over an Airfoil with a Cavity 2011 AIAA Journal
Vol. 49(1), pp. 143-149 
DOI URL 
Abstract: Two-dimensional direct numerical simulation of the flow over a NACA0018 airfoil with a cavity is presented. The low Reynolds number simulations are validated by means of flow visualizations carried out in a water channel. From the simulations, it follows that there are two main regimes of flow inside the cavity. Depending on the angle of attack, the first or the second shear-layer mode (Rossiter tone) is present. The global effect of the cavity on the flow around the airfoil is the generation of vortices that reduce flow separation downstream of the cavity. At high positive angles of attack, the flow separates in front of the cavity, and the separated flow interacts with the cavity, causing the generation of smaller-scale structures and a narrower wake compared with the case when no cavity is present. At certain angles of attack, the numerical results suggest the possibility of a higher lift-to-drag ratio for the airfoil with cavity compared with the airfoil without cavity.
BibTeX:
@article{OlsmanColonius2011,
  author = {Olsman, W. F. J. and Colonius, T.},
  title = {Numerical Simulation of Flow over an Airfoil with a Cavity},
  journal = {AIAA Journal},
  year = {2011},
  volume = {49},
  number = {1},
  pages = {143-149},
  url = {http://colonius.caltech.edu/pdfs/OlsmanColonius2011.pdf},
  doi = {https://doi.org/10.2514/1.J050542}
}
Olsman, W.F.J., Willems, J.F.H., Hirschberg, A., Colonius, T. and Trieling, R.R. Flow around a NACA0018 airfoil with a cavity and its dynamical response to acoustic forcing 2011 Experiments in Fluids
Vol. 51(2), pp. 493-509 
DOI URL 
Abstract: Trapping of vortices in a cavity has been explored in recent years as a drag reduction measure for thick airfoils. If, however, trapping fails, then oscillation of the cavity flow may couple with elastic vibration modes of the airfoil. To examine this scenario, the effect of small amplitude vertical motion on the oscillation of the shear layer above the cavity is studied by acoustic forcing simulating a vertical translation of a modified NACA0018 profile. At low Reynolds numbers based on the chord (O(10(4))), natural instability modes of this shear layer are observed for Strouhal numbers based on the cavity width of order unity. Acoustic forcing sufficiently close to the natural instability frequency induces a strong non-linear response due to lock-in of the shear layer. At higher Reynolds numbers (above 10(5)) for Strouhal number 0.6 or lower, no natural instabilities of the shear layer and only a linear response to forcing were observed. The dynamical pressure difference across the airfoil is then dominated by added mass effects, as was confirmed by numerical simulations.
BibTeX:
@article{OlsmanWillemsHirschbergEtAl2011,
  author = {Olsman, W. F. J. and Willems, J. F. H. and Hirschberg, A. and Colonius, T. and Trieling, R. R.},
  title = {Flow around a NACA0018 airfoil with a cavity and its dynamical response to acoustic forcing},
  journal = {Experiments in Fluids},
  year = {2011},
  volume = {51},
  number = {2},
  pages = {493-509},
  url = {http://colonius.caltech.edu/pdfs/OlsmanWillemsHirschbergEtAl2011.pdf},
  doi = {https://doi.org/10.1007/s00348-011-1065-7}
}
Rodr\iguez, D., Samanta, A., Cavalieri, A., Colonius, T. and Jordan, P. Parabolized stability equation models for predicting large-scale mixing noise of turbulent round jets 2011 17th AIAA/CEAS Aeroacoustics Conference (32nd AIAA Aeroacoustics Conference)  DOI URL 
BibTeX:
@inproceedings{RodriguezSamantaCavalieriEtAl2011,
  author = {Rodr\iguez, Daniel and Samanta, Arnab and Cavalieri, André and Colonius, Tim and Jordan, Peter},
  title = {Parabolized stability equation models for predicting large-scale mixing noise of turbulent round jets},
  booktitle = {17th AIAA/CEAS Aeroacoustics Conference (32nd AIAA Aeroacoustics Conference)},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2011},
  url = {http://colonius.caltech.edu/pdfs/RodriguezSamantaCavalieriEtAl2011.pdf},
  doi = {https://doi.org/10.2514/6.2011-2838}
}
Samanta, A., Appelö, D., Colonius, T., Nott, J. and Hall, J. Comment on "Computational Modeling and Experiments of Natural Convection for a Titan Montgolfiere" Reply 2011 AIAA Journal
Vol. 49(4), pp. 877-878 
DOI URL 
BibTeX:
@article{SamantaAppeloeColoniusEtAl2011,
  author = {Samanta, A. and Appelö, D. and Colonius, T. and Nott, J. and Hall, J.},
  title = {Comment on "Computational Modeling and Experiments of Natural Convection for a Titan Montgolfiere" Reply},
  journal = {AIAA Journal},
  year = {2011},
  volume = {49},
  number = {4},
  pages = {877-878},
  url = {http://colonius.caltech.edu/pdfs/SamantaAppeloeColoniusEtAl2011.pdf},
  doi = {https://doi.org/10.2514/1.J050961}
}
Sanada, T., Ando, K. and Colonius, T. A computational study of high-speed droplet impact 2011 Fluid Dynamics and Material Procsessing
Vol. 7(4), pp. 329-340 
URL 
Abstract: When a droplet impacts a solid surface at high speed, the contact periphery expands very quickly and liquid compressibility plays an important role in the initial dynamics and the formation of lateral jets. The high speed impact results in high pressures that can account for the surface erosion. In this study, we numerically investigated a high speed droplet impacts on a solid wall. The multicomponent Euler equations with the stiffened equation of state are computed using a FV-WENO scheme with an HLLC Riemann solver that accurately captures shocks and interfaces. In order to compare the available theories and experiments, 1D, 2D and axisymmetric solutions are obtained. The generated pressures, shock speeds, and differences in the dimensionality are investigated. In addition, the effect of target compliance is evaluated.
BibTeX:
@article{SanadaAndoColonius2011,
  author = {Sanada, T. and Ando, K. and Colonius, T.},
  title = {A computational study of high-speed droplet impact},
  journal = {Fluid Dynamics and Material Procsessing},
  year = {2011},
  volume = {7},
  number = {4},
  pages = {329-340},
  url = {http://colonius.caltech.edu/pdfs/SanadaAndoColonius2011.pdf}
}
Theofilis, V. and Colonius, T. Special issue on global flow instability and control 2011
Vol. 25(1-4), pp. 1-6 
DOI URL 
Abstract: This special issue is intended to provide a snapshot of current research in the area of "Global Flow Instability and Control". The original papers, and to a certain extent the topic itself, are intimately linked with the series of symposia by the same name that were held in Crete, Greece, between 2001 and 2009. As members of the organizing committees of the Crete symposia, we invited all past participants to contribute, and all papers were reviewed following the strict standards of the journal. This preface gives a brief historical account of events that have shaped ideas in the field over the past decade, followed by a synopsis of the papers published herein.
BibTeX:
@article{TheofilisColonius2011,
  author = {Theofilis, V. and Colonius, T.},
  title = {Special issue on global flow instability and control},
  year = {2011},
  volume = {25},
  number = {1-4},
  pages = {1-6},
  url = {http://colonius.caltech.edu/pdfs/TheofilisColonius2011.pdf},
  doi = {https://doi.org/10.1007/s00162-010-0217-3}
}
Ando, K. Effects of polydispersity in bubbly flows 2010 School: California Institute of Technology  URL 
Abstract: This thesis concerns the dynamics of bubbly flows with a distribution of equilibrium bubble sizes. The main goal is to formulate the physical and numerical models of continuum bubbly flows that enable us to efficiently compute the average mixture dynamics. Numerical simulations are conducted to quantify the effects of bubble size distributions on the averaged dynamics for several model flows.

First, the ensemble-averaged conservation laws for polydisperse bubbly flows are derived. One-way-coupled flow computations are conducted to illustrate that the different-sized bubbles can oscillate with different frequencies. The resulting phase cancellations can be regarded as an apparent damping of the averaged dynamics of polydisperse flows. A high-order-accurate finite-volume method is then developed to compute the flow, paying special attention to issues of wave dispersion and stiffness.

Next, computations of one-dimensional shock propagation through bubbly liquids are performed. The numerical experiments reveal that the bubble size distribution has a profound impact on the averaged shock structure. If the distribution is sufficiently broad, the apparent damping due to the phase cancellations can dominate over the single-bubble-dynamic dissipation (due to thermal, viscous, and compressibility effects) and the averaged shock dynamics become insensitive to the individual bubble dynamics. One-dimensional cloud cavitation caused by fluid-structure interaction is also solved to investigate the collapse of cavitation clouds with both monodisperse and polydisperse nuclei. The phase cancellations among the cavitation bubbles with broad nuclei size distributions are found to eliminate violent cloud collapse in the averaged dynamics.

Finally, shock propagation through a bubbly liquid-filled, deformable tube is considered. The quasi-one-dimensional conservation law that takes into account structural deformation is formulated and steady shock relations are derived. The results are compared to water-hammer experiments; the present shock theory gives better agreement with the measured wave speeds than linear theory. This indicates that the gas-phase nonlinearity needs to be included to accurately predict the propagation speeds of finite-amplitude waves in a deformable tube filled with a bubbly liquid.

BibTeX:
@phdthesis{Ando2010,
  author = {Ando, Keita},
  title = {Effects of polydispersity in bubbly flows},
  school = {California Institute of Technology},
  year = {2010},
  url = {http://resolver.caltech.edu/CaltechTHESIS:05272010-133830557}
}
Ando, K., Sanada, T., Inaba, K., Shepherd, J., Colonius, T. and Brennen, C. Shock Theory of a Bubbly Liquid in a Deformable Tube 2010 7th International Conference on Multiphase Flow  URL 
BibTeX:
@inproceedings{AndoSanadaInabaEtAl2010,
  author = {Ando, K. and Sanada, T. and Inaba, K. and Shepherd, J.E. and Colonius, T. and Brennen, C.E.},
  title = {Shock Theory of a Bubbly Liquid in a Deformable Tube},
  booktitle = {7th International Conference on Multiphase Flow},
  year = {2010},
  url = {http://colonius.caltech.edu/pdfs/AndoSanadaInabaEtAl2010.pdf}
}
Appelö, D., Colonius, T., Hagstrom, T. and Inkman, M. Development of Arbitrary-Order Hermite Methods for Simulation and Analysis of Turbulent Jet Noise 2010
Vol. 6IUTAM Symposium on Computational Aero-Acoustics for Aircraft Noise Prediction, pp. 19-27 
DOI URL 
Abstract: In this short note a brief description of Hermite methods is given. Previous and ongoing development of arbitrary order Hermite methods for the simulation of turbulent jets is also presented. In addition we outline how Hermite methods can be hybridized with discontinuous Galerkin methods to handle boundary conditions in a straightforward way.
BibTeX:
@inproceedings{AppeloeColoniusHagstromEtAl2010,
  author = {Appelö, D. and Colonius, T. and Hagstrom, T. and Inkman, M.},
  title = {Development of Arbitrary-Order Hermite Methods for Simulation and Analysis of Turbulent Jet Noise},
  booktitle = {IUTAM Symposium on Computational Aero-Acoustics for Aircraft Noise Prediction},
  year = {2010},
  volume = {6},
  pages = {19-27},
  url = {http://colonius.caltech.edu/pdfs/AppeloeColoniusHagstromEtAl2010.pdf},
  doi = {https://doi.org/10.1016/j.proeng.2010.09.003}
}
Brès, G.A., Colonius, T. and Fedorov, A.V. Acoustic Properties of Porous Coatings for Hypersonic Boundary-Layer Control 2010 AIAA Journal
Vol. 48(2), pp. 267-274 
DOI URL 
Abstract: Numerical simulations are performed to investigate the interaction of acoustic waves with an array (if equally spaced two-dimensional microcavities on an otherwise flat plate without external boundary-layer flow. This acoustic scattering problem is important in the design of ultrasonic absorptive coatings for hypersonic laminar flow control. The reflection coefficient, characterizing the ratio of the reflected wave amplitude to the incident wave amplitude, is computed as a function of the acoustic wave frequency and angle of incidence, for coatings of different porosities, at various acoustic Reynolds numbers relevant to hypersonic flight. Overall, the numerical results validate predictions from existing theoretical modeling. In general, the amplitude of the reflection coefficient has local minima at some specific frequencies. A simple model to predict these frequencies is presented. The simulations also highlight the presence or resonant acoustic modes caused by coupling of small-scale scattered waves near the coating surface. Finally, the cavity depth and the porosity are identified as the most important parameters for coating design. Guidelines for the choice of these parameters are suggested.
BibTeX:
@article{BresColoniusFedorov2010,
  author = {Brès, G. A. and Colonius, T. and Fedorov, A. V.},
  title = {Acoustic Properties of Porous Coatings for Hypersonic Boundary-Layer Control},
  journal = {AIAA Journal},
  year = {2010},
  volume = {48},
  number = {2},
  pages = {267-274},
  url = {http://colonius.caltech.edu/pdfs/BresColoniusFedorov2010.pdf},
  doi = {https://doi.org/10.2514/1.40811}
}
Brès, G., Williams, D. and Colonius, T. Numerical Simulations of Natural and Actuated Flow over a 3-D, Low-Aspect-Ratio Airfoil 2010 40th Fluid Dynamics Conference and Exhibit  DOI URL 
BibTeX:
@inproceedings{BresWilliamsColonius2010,
  author = {Brès, Guillaume and Williams, David and Colonius, Tim},
  title = {Numerical Simulations of Natural and Actuated Flow over a 3-D, Low-Aspect-Ratio Airfoil},
  booktitle = {40th Fluid Dynamics Conference and Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2010},
  url = {http://colonius.caltech.edu/pdfs/BresWilliamsColonius2010.pdf},
  doi = {https://doi.org/10.2514/6.2010-4713}
}
Chen, K.K., Colonius, T. and Taira, K. The leading-edge vortex and quasisteady vortex shedding on an accelerating plate 2010 Physics of Fluids
Vol. 22(3) 
DOI URL 
Abstract: A computational inquiry focuses on leading-edge vortex (LEV) growth and shedding during acceleration of a two-dimensional flat plate at a fixed 10 degrees-60 degrees angle of attack and low Reynolds number. The plate accelerates from rest with a velocity given by a power of time ranging from 0 to 5. During the initial LEV growth, subtraction of the added mass lift from the computed lift reveals an LEV-induced lift augmentation evident across all powers and angles of attack. For the range of Reynolds numbers considered, a universal time scale exists for the peak when alpha >= 30 degrees, with augmentation lasting about four to five chord lengths of translation. This time scale matches well with the half-stroke of a flying insect. An oscillating pattern of leading- and trailing-edge vortex shedding follows the shedding of the initial LEV. The nondimensional frequency of shedding and lift coefficient minima and maxima closely match their values in the absence of acceleration. These observations support a quasisteady theory of vortex shedding, where dynamics are determined primarily by velocity and not acceleration. Finally, the nondimensional vortex formation time is found to be a function of the Reynolds number, but only weakly when the Reynolds number is high.
BibTeX:
@article{ChenColoniusTaira2010,
  author = {Chen, K. K. and Colonius, T. and Taira, K.},
  title = {The leading-edge vortex and quasisteady vortex shedding on an accelerating plate},
  journal = {Physics of Fluids},
  year = {2010},
  volume = {22},
  number = {3},
  url = {http://colonius.caltech.edu/pdfs/ChenColoniusTaira2010.pdf},
  doi = {https://doi.org/10.1063/1.3327282}
}
Colonius, T., Samanta, A. and Guðmundsson, K. Parabolized stability equation models of large-scale jet mixing noise 2010
Vol. 6IUTAM Symposium on Computational Aero-Acoustics for Aircraft Noise Prediction, pp. 64-73 
DOI URL 
Abstract: We report on the development of parabolized stability equation models to predict the evolution of low frequencies, large-scale wavepacket structures in turbulent jets and their radiated sound. We consider computations and data corresponding to high subsonic and supersonic jets from circular nozzles. Previous methods are extended to consider nonlinear interactions amongst the waves and use a Kirchhoff-surface type approach to project the near-field wavepacket amplitudes to the far-field. Linear PSE, whose initial conditions are chosen to provide an overall amplitude reference, show excellent agreement for the wavepacket amplitudes and phases with microphone array data just outside the jet shear layers, especially when the microphone data are processed to filter out contributions from uncorrelated fluctuations. Far-field sound predictions based on the linear PSE are also in reasonable agreement with far-field data. In order to investigate nonlinearity, we use an LES database to evaluate initial conditions for the PSE modes, and then compare their later evolution along the jet. Preliminary cases show some sensitivity to the initial amplitudes and their phases, and that nonlinear effects may be important in predicting the far-field sound based on the initial (near-nozzle) spectrum of disturbances.
BibTeX:
@inproceedings{ColoniusSamantaGuhmundsson2010,
  author = {Colonius, T. and Samanta, A. and Guðmundsson, K.},
  title = {Parabolized stability equation models of large-scale jet mixing noise},
  booktitle = {IUTAM Symposium on Computational Aero-Acoustics for Aircraft Noise Prediction},
  year = {2010},
  volume = {6},
  pages = {64-73},
  url = {http://colonius.caltech.edu/pdfs/ColoniusSamantaGuhmundsson2010.pdf},
  doi = {https://doi.org/10.1016/j.proeng.2010.09.008}
}
Franck, J.A. and Colonius, T. Compressible Large-Eddy Simulation of Separation Control on a Wall-Mounted Hump 2010 AIAA Journal
Vol. 48(6), pp. 1098-1107 
DOI URL 
Abstract: Compressible large-eddy simulations of turbulent flow over a wall-mounted hump with active flow control are performed and compared with previous experiments. The flow is characterized by the unsteady separation before the steep trailing edge, which naturally reattaches downstream of the hump to form an unsteady turbulent separation bubble. The low Mach number large-eddy simulation demonstrated a good prediction of surface pressure coefficient, separation-bubble length, and velocity profiles compared with experiments. The effect of compressibility on the baseline flow is documented and analyzed and is found to increase the separation-bubble size, due to a reduced growth rate. Control is applied just before the natural separation point via steady suction and zero-net-mass-flux oscillatory forcing, and steady suction is shown to be more effective in decreasing the size of the separation bubble and pressure drag for the control parameters investigated. Controlled flow at a compressible subsonic Mach number is applied, and found to be slightly less effective than the same control parameters at low Mach numbers.
BibTeX:
@article{FranckColonius2010,
  author = {Franck, J. A. and Colonius, T.},
  title = {Compressible Large-Eddy Simulation of Separation Control on a Wall-Mounted Hump},
  journal = {AIAA Journal},
  year = {2010},
  volume = {48},
  number = {6},
  pages = {1098-1107},
  url = {http://colonius.caltech.edu/pdfs/FranckColonius2010.pdf},
  doi = {https://doi.org/10.2514/1.44756}
}
Guðmundsson, K. Instability Wave Models of Turbulent Jets from Round and Serrated Nozzles 2010 School: California Institute of Technology  URL 
Abstract: In this thesis we study pressure fluctuations associated with large-scale coherent structures in turbulent round and serrated jets. Linear disturbances to the turbulent mean flow of the round jet are modeled via linear stability analysis and the Parabolized Stability Equations (PSE). We show that PSE provides better agreement with near-field microphone-array data at low frequencies than previous models based on linear stability theory. We examine the extent to which microphone data is contaminated by fluctuations uncorrelated with large-scale structures. By filtering out the uncorrelated fluctuations, via the proper orthogonal decomposition (POD), better agreement between data and theory is obtained. We next extend the linear stability analysis of round jets to include the effects of azimuthal inhomogeneities of serrated jets. We solve the resulting system of equations and find new modes, associated with the streamwise vorticity of the serrated-jet mean flow. All unstable modes of the serrated jet are stabilized, potentially explaining the noise reduction achieved by such jets. We also compare these predictions to POD-filtered microphone measurements, generally finding good agreement.
BibTeX:
@phdthesis{Guhmundsson2010,
  author = {Guðmundsson, Kristján},
  title = {Instability Wave Models of Turbulent Jets from Round and Serrated Nozzles},
  school = {California Institute of Technology},
  year = {2010},
  url = {http://resolver.caltech.edu/CaltechTHESIS:01242010-111852941}
}
Joe, W.T. Optimized feedback control of vortex shedding on an inclined flat plate 2010 School: California Institute of Technology  URL 
Abstract: This thesis examines flow control and the potentially favorable effects of feedback, associated with unsteady actuation in separated flows over airfoils.
The objective of the flow control is to enhance lift at post-stall angles of attack by changing the dynamics of the wake vortices. We present results from a numerical study of unsteady actuation on a two-dimensional flat plate at post-stall angles of attack at Reynolds number (Re) of 300 and 3000. At Re=300, the control waveform is optimized and a feedback strategy is developed to optimize the phase of the control relative to the lift with either a sinusoidal or the optimized waveform, resulting in a high-lift limit cycle of vortex shedding. Also at Re=3000, we show that certain frequencies and actuator waveforms lead to stabl(high-lift) limit cycles, in which the flow is phase locked to the actuation.

First, a two-dimensional flat plate model at a high angle of attack at a Re of 300 is considered. We design the feedback to slightly adjust the frequency and/or phase of actuation to lock it to a particular phase of the lift, thus achieving a phase-locked flow with the maximal period-averaged lift over every cycle of acutation.

With the sinusoidal forcing and feedback, we show that it is possible to optimize the phase of the control relative to the lift in order to achieve the highest possible period-averaged lift in a consistent fashion. However, continuous sinusoidal forcing could be adding circulation when it is unnecessary, or undesirable. Thus we employ an adjoint-based optimization in order to find the waveform (time history of the jet velocty) that maximizes the lift for a given actuation amplitude. The adjoint of the linearized perturbed equations is solved backwards in time to obtain the gradient of the lift to changes in actuation (the jet velocity), and this information is used to iteratively improve the controls.

Optimal control provides a periodic control waveform, resulting in high lift shedding cycle with minimal control input. However, if applied in open loop, the flow fails to phase lock onto the optimal waveform, degrading the lift performance. Thus, the optimized waveform is also implemented in a closed-loop controller where the control signal is shifted or deformed periodically to adjust to the (instantaneous) frequency of the lift fluctuations.
The feedback utilizes a narrowband filter and an Extended Kalman Filter to robustly estimate the phase of vortex shedding and achieve phase-locked, high lift flow states.
Feedback control of the optimized waveform is able to reproduce the high-lift limit cycle from the optimization, but starting from an arbitrary phase of the baseline limit cycle.

Finally, we apply the tools developed and knowledge gained at Re=300 to a Re of 3000 on a thin airfoil with a thickness-to-chord ratio of 4%, which were chosen to match the experimental studies of Greenblatt et al. (2008).
We consider more detailed time-dependent aspects of the lift and corresponding flow fields, particularly the flow structures at the minimum and maximum lift, and the phase of pulses relative to the lift, in order to more precisely compare different actuated flow fields and distinguish the differences responsible for higher or lower instantaneous lift, along with identifying different vortex evolutions.
We consider two representative angles of attack, 10 and 20 degrees, and investigate the lift enhancement and which combinations of forcing frequency and duty cycle lead to phase-locked flow. Finally, we show that for certain frequencies and actuator waveforms, there occur stable limit cycles in which the flow is phase locked to the actuation.

BibTeX:
@phdthesis{Joe2010,
  author = {Joe, Won Tae},
  title = {Optimized feedback control of vortex shedding on an inclined flat plate},
  school = {California Institute of Technology},
  year = {2010},
  url = {http://resolver.caltech.edu/CaltechTHESIS:06072010-131025711}
}
Joe, W.T., Colonius, T. and MacMynowski, D.G. Optimized Waveforms for Feedback Control of Vortex Shedding 2010
Vol. 108Active Flow Control II, pp. 391-404 
DOI URL 
Abstract: Optimal control theory is combined with the numerical simulation of an incompressible viscous flow to control vortex shedding in order to maximize lift. A two-dimensional flat plate model is considered at a high angle of attack and a Reynolds number of 300. Actuation is provided by unsteady mass injection near the trailing edge and is modeled by a compact body force. The adjoint of the linearized perturbed equations is solved backwards in time to obtain the gradient of the lift to changes in actuation (the jet velocity), and this information is used to iteratively improve the controls. The optimized control waveform is nearly periodic and locked to vortex shedding. We compare the results with sinusoidal open- and closed-loop control and observe that the optimized control is able to achieve higher lift than the sinusoidal forcing with more than 50% lower momentum coefficients. The optimized waveform is also implemented in a simple closed-loop controller where the control signal is shifted or deformed periodically to adjust to the (instantaneous) frequency of the lift fluctuations. The feedback utilizes a narrowband filter and an Extended Kalman Filter to robustly estimate the phase of vortex shedding and achieve phase-locked, high lift flow states.
BibTeX:
@inproceedings{JoeColoniusMacMynowski2010,
  author = {Joe, W. T. and Colonius, T. and MacMynowski, D. G.},
  title = {Optimized Waveforms for Feedback Control of Vortex Shedding},
  booktitle = {Active Flow Control II},
  year = {2010},
  volume = {108},
  pages = {391-404},
  url = {http://colonius.caltech.edu/pdfs/JoeColoniusMacMynowski2010.pdf},
  doi = {https://doi.org/10.1007/978-3-642-11735-0_25}
}
Khalighi, Y., Ham, F., Moin, P., Lele, S.K., Colonius, T., Schlinker, R.H., Reba, R.A. and Simonich, J. Unstructured Large Eddy Simulation Technology for Prediction and Control of Jet Noise 2010 Proceedings of the Asme Turbo Expo 2010, Vol 1, pp. 57-70  DOI URL 
BibTeX:
@inproceedings{KhalighiHamMoinEtAl2010,
  author = {Khalighi, Y. and Ham, F. and Moin, P. and Lele, S. K. and Colonius, T. and Schlinker, R. H. and Reba, R. A. and Simonich, J.},
  title = {Unstructured Large Eddy Simulation Technology for Prediction and Control of Jet Noise},
  booktitle = {Proceedings of the Asme Turbo Expo 2010, Vol 1},
  year = {2010},
  pages = {57-70},
  url = {http://colonius.caltech.edu/pdfs/KhalighiHamMoinEtAl2010.pdf},
  doi = {https://doi.org/10.1115/gt2010-22306}
}
Krimmel, J. Numerical simulation of wave focusing and scattering in shock wave lithotripsy 2010 School: California Institute of Technology  URL 
Abstract: In this work we simulate shock wave focusing and scattering that occurs during shock wave lithotripsy, a noninvasive medical treatment for kidney stone disease. Shock waves are generated outside the body of the patient and are focused at the kidney stone with the intention of pulverizing the stone while it remains inside the patient. The patient can then ostensibly pass the debris naturally. We use a multidimensional second-order method of the Godunov type with slope limiters and shock capturing capability to solve the inviscid Euler equations. Because we begin with the fundamental statements of conservation of mass, momentum, and energy, we simulate all the relevant acoustics occurring during a typical treatment.

Lithotripters, the machines that generate and focus shock waves, can be classified according to the mechanism of shock generation. In this work, we simulate three different types of lithotripters: electrohydraulic, piezoelectric, and electromagnetic. We choose one representative of each lithotripter type: the Dornier HM3, a research piezoelectric lithotripter array, and the XX-Es, respectively. We first study a model of the in vitro setting for each lithotripter, where shock waves are generated and focus in a bath of pure water. Next, we introduce different heterogeneous materials near the focus of the lithotripter to model the effect of the body of an actual patient, i.e., the in vivo condition. We use two approaches in this modeling effort. One approach is to use simple geometrical models for the body cavity and kidney that we created ourselves. The other approach is to import real anatomical data made available from the VOXEL-MAN Group.

In studying the focal region acoustics, we specifically examine the maximum calculated pressures. These pressures represent the forces that will ultimately cause the kidney stone to break. We also study the pulse intensity integral, i.e., the energy density carried by the focusing shock wave. In addition to these pressures and energy densities, we are interested in investigating how soft tissue in the focal region may potentially be damaged by the resulting wavefields. We isolate two mechanisms that are thought to be important in soft tissue injury: shearing and cavitation. We calculate estimates for the maximum principal normal and shear strains in the focal region in addition to the corresponding strain rates and use these as metrics for the potential for damage via shearing. We study the calculated negative pressure fields in this region as a surrogate for potential damage caused by cavitation.

BibTeX:
@phdthesis{Krimmel2010,
  author = {Krimmel, Jeffrey},
  title = {Numerical simulation of wave focusing and scattering in shock wave lithotripsy},
  school = {California Institute of Technology},
  year = {2010},
  url = {http://resolver.caltech.edu/CaltechTHESIS:05282010-150032204}
}
Krimmel, J., Colonius, T. and Tanguay, M. Simulation of the effects of cavitation and anatomy in the shock path of model lithotripters 2010 Urological Research
Vol. 38(6), pp. 505-518 
DOI URL 
Abstract: We report on recent efforts to develop predictive models for the pressure and other flow variables in the focal region of shock wave lithotripters. Baseline simulations of three representative lithotripters (electrohydraulic, electromagnetic, and piezoelectric) compare favorably with in vitro experiments (in a water bath). We proceed to model and investigate how shock focusing is altered by the presence of material interfaces associated with different types of tissue encountered along the shock path, and by the presence of cavitation bubbles that are excited by tensile pressures associated with the focused shock wave. We use human anatomical data, but simplify the description by assuming that the tissue behaves as a fluid, and by assuming cylindrical symmetry along the shock path. Scattering by material interfaces is significant, and regions of high pressure amplitudes (both compressive and tensile) are generated almost 4 cm postfocus. Bubble dynamics generate secondary shocks whose strength depends on the density of bubbles and the pulse repetition frequency (PRF). At sufficiently large densities, the bubbles also attenuate the shock. Together with experimental evidence, the simulations suggest that high PRF may be counterproductive for stone comminution. Finally, we discuss how the lithotripter simulations can be used as input to more detailed physical models that attempt to characterize the mechanisms by which collapsing cavitation models erode stones, and by which shock waves and bubbles may damage tissue.
BibTeX:
@article{KrimmelColoniusTanguay2010,
  author = {Krimmel, J. and Colonius, T. and Tanguay, M.},
  title = {Simulation of the effects of cavitation and anatomy in the shock path of model lithotripters},
  journal = {Urological Research},
  year = {2010},
  volume = {38},
  number = {6},
  pages = {505-518},
  url = {http://colonius.caltech.edu/pdfs/KrimmelColoniusTanguay2010.pdf},
  doi = {https://doi.org/10.1007/s00240-010-0332-z}
}
Ladeinde, F., Alabi, K., Colonius, T., Guðmundsson, K., Schlinker, R. and Reba, R. An Integrated RANS-PSE-Wave Packet Tool for the Prediction of Subsonic and Supersonic Jet Noise 2010 16th AIAA/CEAS Aeroacoustics Conference  DOI URL 
BibTeX:
@inproceedings{LadeindeAlabiColoniusEtAl2010,
  author = {Ladeinde, Foluso and Alabi, Ken and Colonius, Tim and Guðmundsson, Kristján and Schlinker, Robert and Reba, Ramons},
  title = {An Integrated RANS-PSE-Wave Packet Tool for the Prediction of Subsonic and Supersonic Jet Noise},
  booktitle = {16th AIAA/CEAS Aeroacoustics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2010},
  url = {http://colonius.caltech.edu/pdfs/LadeindeAlabiColoniusEtAl2010.pdf},
  doi = {https://doi.org/10.2514/6.2010-4021}
}
Reba, R., Narayanan, S. and Colonius, T. Wave-packet models for large-scale mixing noise 2010 International Journal of Aeroacoustics
Vol. 9(4-5), pp. 533-557 
DOI URL 
Abstract: A wave-packet Ansatz is used to model jet noise generation by large-scale turbulence. In this approach, an equivalent source is defined based on the two-point space-time correlation of hydrodynamic pressure on a conical surface surrounding the jet plume. The surface is sufficiently near the turbulent flow region to be dominated by non-propagating hydrodynamic signatures of large-scale turbulent structures, yet sufficiently far that linear behavior can be assumed in extending the near-field pressure to the acoustic field. In the present study, a 78-microphone array was used to measure hydrodynamic pressure on the conical surface in order to identify parameters for the model and to validate the approach. Six microphones were distributed in the azimuthal direction at each of 13 axial locations spanning the first 8 jet diameters, allowing decomposition of azimuthal modes m = 0 and m = 1. We show that a source model based on a Gaussian correlation function provides a consistently good representation of the noise source attributed to large-scale structures. The results provide evidence that large-scale wave-like structures, known to dominate aft radiation at supersonic phase speeds, are also relevant at subsonic speeds.
BibTeX:
@article{RebaNarayananColonius2010,
  author = {Reba, R. and Narayanan, S. and Colonius, T.},
  title = {Wave-packet models for large-scale mixing noise},
  journal = {International Journal of Aeroacoustics},
  year = {2010},
  volume = {9},
  number = {4-5},
  pages = {533-557},
  url = {http://colonius.caltech.edu/pdfs/RebaNarayananColonius2010.pdf},
  doi = {https://doi.org/10.1260/1475-472x.9.4-5.533}
}
Samanta, A., Appelö, D., Colonius, T., Nott, J. and Hall, J. Computational Modeling and Experiments of Natural Convection for a Titan Montgolfiere 2010 AIAA Journal
Vol. 48(5), pp. 1007-1016 
DOI URL 
Abstract: Computational models are developed to predict the natural convection heat transfer and buoyancy for a Montgolfiere under conditions relevant to the Titan atmosphere. Idealized single- and double-walled balloon geometries are simulated using algorithms suitable for both laminar and (averaged) turbulent convection. Steady-state performance results are compared with existing heat transfer coefficient correlations. The laminar results, in particular, are used to test the validity of the correlations in the absence of uncertainties associated with turbulence modeling. Some discrepancies are observed, which appear to he primarily associated with temperature non-uniformity on the balloon surface. The predicted buoyancy for both the single- and double-walled balloons in the turbulent convection regime, predicted with standard two-equation
turbulence models, showed trends similar to those with the empirical correlations. There was also good agreement with recently conducted experiments in a cryogenic facility designed to simulate the Titan atmosphere.
BibTeX:
@article{SamantaAppeloeColoniusEtAl2010,
  author = {Samanta, A. and Appelö, D. and Colonius, T. and Nott, J. and Hall, J.},
  title = {Computational Modeling and Experiments of Natural Convection for a Titan Montgolfiere},
  journal = {AIAA Journal},
  year = {2010},
  volume = {48},
  number = {5},
  pages = {1007-1016},
  url = {http://colonius.caltech.edu/pdfs/SamantaAppeloeColoniusEtAl2010.pdf},
  doi = {https://doi.org/10.2514/1.45854}
}
Sanada, K., Ando, K. and Colonius, T. Numerical Analysis of High Speed Droplet Impact 2010 7th International Conference on Multiphase Flow, Tampa, FL  URL 
BibTeX:
@inproceedings{SanadaAndoColonius2010,
  author = {Sanada, K. and Ando, K. and Colonius, T.},
  title = {Numerical Analysis of High Speed Droplet Impact},
  booktitle = {7th International Conference on Multiphase Flow, Tampa, FL},
  year = {2010},
  url = {http://colonius.caltech.edu/pdfs/SanadaAndoColonius2010.pdf}
}
Taira, K. and Colonius, T. Effect of Tip Vortices in Low-Reynolds-Number Poststall Flow Control (Correction to vol 47, pg 749, 2009) 2010 AIAA Journal
Vol. 48(3), pp. 702-702 
DOI URL 
Abstract: We numerically investigate the application of steady blowing to three-dimensional stalled flows around lowaspect-ratio rectangular flat-plate wings at a Reynolds number of 300. The objective of this study is to explore techniques to enhance lift by directly modifying the dynamics of the wake vortices. Out of various combinations of forcing location and direction considered, we identify two configurations that provide significant lift enhancement. In these cases, actuation appears to strengthen the tip vortices for increased downward induced velocity upon the leading-edge vortices. This in turn moves the low-pressure core directly above the top surface of the wing to greatly enhance lift.
BibTeX:
@article{TairaColonius2010,
  author = {Taira, K. and Colonius, T.},
  title = {Effect of Tip Vortices in Low-Reynolds-Number Poststall Flow Control (Correction to vol 47, pg 749, 2009)},
  journal = {AIAA Journal},
  year = {2010},
  volume = {48},
  number = {3},
  pages = {702-702},
  url = {http://colonius.caltech.edu/pdfs/TairaColonius2010.pdf},
  doi = {https://doi.org/10.2514/1.48009}
}
Taira, K., Rowley, C. and Colonius, T. Feedback Control of High-Lift State for A Low-Aspect-Ratio Wing 2010 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition  DOI URL 
BibTeX:
@inproceedings{TairaRowleyColonius2010,
  author = {Taira, Kunihiko and Rowley, Clarence and Colonius, Tim},
  title = {Feedback Control of High-Lift State for A Low-Aspect-Ratio Wing},
  booktitle = {48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2010},
  url = {http://colonius.caltech.edu/pdfs/TairaRowleyColonius2010.pdf},
  doi = {https://doi.org/10.2514/6.2010-357}
}
Taira, K., Rowley, C.W. and Colonius, T. Lock-On to a High-Lift State with Oscillatory Forcing in a Three-Dimensional Wake Flow 2010
Vol. 108Active Flow Control II, pp. 81-93 
DOI URL 
Abstract: Flow control is applied to a three-dimensional post-stall flow around a rectangular low-aspect-ratio wing. Steady actuation is used to examine effective flow control setups that modify the vortex dynamics in the wake and achieve increase in lift. For one of the setups, oscillatory forcing is then used to examine the influence of actuation frequency. It is found that sinusoidal actuation requires less momentum to the flow field to achieve lift increase compared to steady momentum injection. There are two observed ranges of forcing frequency at which the flow locks onto period-one and period-two high-lift states. Discussions of the ongoing work on stabilizing separated flow about these periodic high-lift states are offered.
BibTeX:
@inproceedings{TairaRowleyColonius2010a,
  author = {Taira, K. and Rowley, C. W. and Colonius, T.},
  title = {Lock-On to a High-Lift State with Oscillatory Forcing in a Three-Dimensional Wake Flow},
  booktitle = {Active Flow Control II},
  year = {2010},
  volume = {108},
  pages = {81-93},
  url = {http://colonius.caltech.edu/pdfs/TairaRowleyColonius2010a.pdf},
  doi = {https://doi.org/10.1007/978-3-642-11735-0_6}
}
Taira, K., Rowley, C.W., Colonius, T. and Williams, D.R. Lift Enhancement for Low-Aspect-Ratio Wings with Periodic Excitation 2010 AIAA Journal
Vol. 48(8), pp. 1785-1790 
DOI URL 
Abstract: In an effort to enhance lift on low-aspect-ratio rectangular flat-plate wings in low-Reynolds-number poststall flows, periodic injection of momentum is considered along the trailing edge in this numerical study. The purpose of actuation is not to reattach the flow but to change the dynamics of the wake vortices such that the resulting lift force is increased. Periodic forcing is observed to be effective in increasing lift for various aspect ratios and angles of attack, achieving a similar lift enhancement attained by steady forcing with less momentum input. Through the investigation on the influence of the actuation frequency, it is also found that there exists a frequency at which the flow locks on to a time-periodic high-lift state.
BibTeX:
@article{TairaRowleyColoniusEtAl2010,
  author = {Taira, K. and Rowley, C. W. and Colonius, T. and Williams, D. R.},
  title = {Lift Enhancement for Low-Aspect-Ratio Wings with Periodic Excitation},
  journal = {AIAA Journal},
  year = {2010},
  volume = {48},
  number = {8},
  pages = {1785-1790},
  url = {http://colonius.caltech.edu/pdfs/TairaRowleyColoniusEtAl2010.pdf},
  doi = {https://doi.org/10.2514/1.J050248}
}
Williams, D., Kerstens, W., Pfeiffer, J., King, R. and Colonius, T. Closed Loop Control of a Wing's Lift for 'Gust' Suppression 2010 5th Flow Control Conference  DOI URL 
BibTeX:
@inproceedings{WilliamsKerstensPfeifferEtAl2010a,
  author = {Williams, David and Kerstens, Wesley and Pfeiffer, Jens and King, Rudibert and Colonius, Tim},
  title = {Closed Loop Control of a Wing's Lift for 'Gust' Suppression},
  booktitle = {5th Flow Control Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2010},
  url = {http://colonius.caltech.edu/pdfs/WilliamsKerstensPfeifferEtAl2010a.pdf},
  doi = {https://doi.org/10.2514/6.2010-4969}
}
Williams, D., Kerstens, W., Pfeiffer, J., King, R. and Colonius, T. Unsteady Lift Suppression with a Robust Closed Loop Controller 2010
Vol. 108Active Flow Control II, pp. 19-30 
DOI URL 
Abstract: The ability to control lift in unsteady flows using active flow control is examined experimentally with a three-dimensional, low-aspect-ratio wing and pulsed-blowing actuators as the test article. An unsteady flow wind tunnel is used to generate step-like and harmonic oscillations in flow speed and the corresponding fluctuating lift force on the wing. A 'black box' model of the wing response to actuation is obtained using conventional system identification techniques. A robust H(infinity) controller is designed with a mixed sensitivity loop-shaping technique, whose objective was to maintain a constant lift in the unsteady flow. The controller is shown to be capable of significant reductions in lift fluctuations given step, harmonic and random input disturbance conditions.
BibTeX:
@inproceedings{WilliamsKerstensPfeifferEtAl2010,
  author = {Williams, D. and Kerstens, W. and Pfeiffer, J. and King, R. and Colonius, T.},
  title = {Unsteady Lift Suppression with a Robust Closed Loop Controller},
  booktitle = {Active Flow Control II},
  year = {2010},
  volume = {108},
  pages = {19-30},
  url = {http://colonius.caltech.edu/pdfs/WilliamsKerstensPfeifferEtAl2010.pdf},
  doi = {https://doi.org/10.1007/978-3-642-11735-0_2}
}
Williams, D., Kerstens, W., Pfeiffer, J., King, R., Tadmor, G., Colonius, T., Buntain, S. and Quach, V. Closed-Loop Control of a Wing in an Unsteady Flow 2010 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition  DOI URL 
BibTeX:
@inproceedings{WilliamsKerstensPfeifferEtAl2010b,
  author = {Williams, David and Kerstens, Wesley and Pfeiffer, Jens and King, Rudibert and Tadmor, Gilead and Colonius, Tim and Buntain, Seth and Quach, Vien},
  title = {Closed-Loop Control of a Wing in an Unsteady Flow},
  booktitle = {48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2010},
  url = {http://colonius.caltech.edu/pdfs/WilliamsKerstensPfeifferEtAl2010b.pdf},
  doi = {https://doi.org/10.2514/6.2010-358}
}
Ando, K., Colonius, T. and Brennen, C. Shock propagation in polydisperse bubbly flows 2009 CAV2009: Seventh International Symposium on Caviation  URL 
BibTeX:
@inproceedings{AndoColoniusBrennen2009a,
  author = {Ando, K. and Colonius, T. and Brennen, C.E.},
  title = {Shock propagation in polydisperse bubbly flows},
  booktitle = {CAV2009: Seventh International Symposium on Caviation},
  year = {2009},
  url = {http://colonius.caltech.edu/pdfs/AndoColoniusBrennen2009a.pdf}
}
Ando, K., Colonius, T. and Brennen, C.E. Improvement of acoustic theory of ultrasonic waves in dilute bubbly liquids 2009 Journal of the Acoustical Society of America
Vol. 126(3), pp. El69-El74 
DOI URL 
Abstract: The theory of the acoustics of dilute bubbly liquids is reviewed, and the dispersion relation is modified by including the effect of liquid compressibility on the natural frequency of the bubbles. The modified theory is shown to more accurately predict the trend in measured attenuation of ultrasonic waves. The model limitations associated with such high-frequency waves are discussed.
BibTeX:
@article{AndoColoniusBrennen2009,
  author = {Ando, K. and Colonius, T. and Brennen, C. E.},
  title = {Improvement of acoustic theory of ultrasonic waves in dilute bubbly liquids},
  journal = {Journal of the Acoustical Society of America},
  year = {2009},
  volume = {126},
  number = {3},
  pages = {El69-El74},
  url = {http://colonius.caltech.edu/pdfs/AndoColoniusBrennen2009.pdf},
  doi = {https://doi.org/10.1121/1.3182858}
}
Appelö, D. and Colonius, T. A high-order super-grid-scale absorbing layer and its application to linear hyperbolic systems 2009 Journal of Computational Physics
Vol. 228(11), pp. 4200-4217 
DOI URL 
Abstract: We continue the development of the super-grid-scale model initiated in [T. Colonius, H. Ran, A super-grid-scale model for simulating compressible flow on unbounded domains. J. Comput. Phys. 182 (1) (2002) 191-212] and consider its application to linear hyperbolic systems. The super-grid-scale model consists of two parts: reduction of an unbounded to a bounded domain by a smooth coordinate transformation and a damping of those scales. For linear problems the super-grid scales are analogous to spurious numerical waves. We damp these waves by high-order undivided differences. We compute reflection coefficients for different orders of the damping and find that significant improvements are obtained when high-order damping is used. In numerical experiments with Maxwell's equations, we show that when the damping is of high order, the error from the boundary condition converges at the order of the interior scheme. We also demonstrate that the new method achieves perfectly matched layer-like accuracy. When applied to linear hyperbolic systems the stability of the super-grid-scale method follows from its construction. This makes our method particularly suitable for problems for which perfectly matched layers are unstable. We present results for two such problems: elastic waves in anisotropic media and isotropic elastic waves in wave guides with traction-free surfaces.
BibTeX:
@article{AppeloeColonius2009,
  author = {Appelö, D. and Colonius, T.},
  title = {A high-order super-grid-scale absorbing layer and its application to linear hyperbolic systems},
  journal = {Journal of Computational Physics},
  year = {2009},
  volume = {228},
  number = {11},
  pages = {4200-4217},
  url = {http://colonius.caltech.edu/pdfs/AppeloeColonius2009.pdf},
  doi = {https://doi.org/10.1016/j.jcp.2009.02.030}
}
Appelo, D., Colonius, T., Nott, J. and Hall, J. Computational Modeling and Experiments of Natural Convection for a Titan Montgolfiere 2009 AIAA Balloon Systems Conference  DOI URL 
BibTeX:
@inproceedings{AppeloColoniusNottEtAl2009,
  author = {Appelo, Daniel and Colonius, Tim and Nott, Julian and Hall, Jeffrey},
  title = {Computational Modeling and Experiments of Natural Convection for a Titan Montgolfiere},
  booktitle = {AIAA Balloon Systems Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2009},
  url = {http://colonius.caltech.edu/pdfs/AppeloColoniusNottEtAl2009.pdf},
  doi = {https://doi.org/10.2514/6.2009-2806}
}
Brès, G., Inkman, M., Colonius, T. and Fedorov, A. Alternate Designs of Ultrasonic Absorptive Coatings for Hypersonic Boundary Layer Control 2009 39th AIAA Fluid Dynamics Conference  DOI URL 
BibTeX:
@inproceedings{BresInkmanColoniusEtAl2009,
  author = {Brès, Guillaume and Inkman, Matthew and Colonius, Tim and Fedorov, Alexander},
  title = {Alternate Designs of Ultrasonic Absorptive Coatings for Hypersonic Boundary Layer Control},
  booktitle = {39th AIAA Fluid Dynamics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2009},
  url = {http://colonius.caltech.edu/pdfs/BresInkmanColoniusEtAl2009.pdf},
  doi = {https://doi.org/10.2514/6.2009-4217}
}
Franck, J. Large-eddy simulation of flow separation and control on a wall-mounted hump 2009 School: California Institute of Technology  URL 
Abstract: Active flow control techniques such as synthetic jets have been successful in increasing the performance of naturally separating flows on post-stall airfoils, bluff body shedding, and internal flows such as wide-angle diffusers. However, in order to implement robust control techniques there is a need for accurate computational tools capable of predicting unsteady separation and control at high Reynolds numbers. This thesis developed a compressible large-eddy simulation (LES) and validated it by simulating the turbulent flow over a wall-mounted hump. The flow is characterized by an unsteady, turbulent recirculation region along the trailing edge of the geometry, and is simulated at a Reynolds number of 500,000. Active flow control is applied just before the natural separation point via steady suction and zero-net mass flux oscillatory forcing. The addition of control is shown to be effective in decreasing the size of the separation bubble and pressure drag. LES baseline and controlled results are validated against previously performed experiments by Seifert and Pack and those performed for the NASA Langley Workshop on Turbulent Flow Separation and Control. Three test cases are explored to determine the effect of explicit filtering and the Smagorinsky subgrid scale model on the average flow and turbulent statistics. The flow physics and the control effectiveness are investigated at two Mach numbers, M=0.25 and M=0.6. Compressibility is shown to increase the separation bubble length in the baseline case, but does not significantly change the effectiveness of the control. In terms of decreasing drag on the wall-mounted hump model, steady suction is more effective than oscillatory control, but both control techniques are effective in reducing the separation bubble length. Two-dimensional direct numerical simulations (DNS) of the wall-mounted hump flow are also presented, and the results show different baseline flow features than the 3D LES. However the controlled 2D flow gives an indication of the most receptive actuation frequencies around twice that of the natural shedding frequency. Two regimes of reduced actuation frequency are also explored with the 3D LES. It is found that the low frequency actuation is successful in reducing the separation bubble length, but high frequency actuation produces an average flow comparable to the baseline case, and does not result in drag or separation bubble length reduction.
BibTeX:
@phdthesis{Franck2009,
  author = {Franck, Jennifer},
  title = {Large-eddy simulation of flow separation and control on a wall-mounted hump},
  school = {California Institute of Technology},
  year = {2009},
  url = {http://resolver.caltech.edu/CaltechETD:etd-06022009-183247}
}
Franck, J. and Colonius, T. Oscillatory Control and the Effects of Actuation Frequency on a Wall-Mounted Hump 2009 39th AIAA Fluid Dynamics Conference  DOI URL 
BibTeX:
@inproceedings{FranckColonius2009,
  author = {Franck, Jennifer and Colonius, Tim},
  title = {Oscillatory Control and the Effects of Actuation Frequency on a Wall-Mounted Hump},
  booktitle = {39th AIAA Fluid Dynamics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2009},
  url = {http://colonius.caltech.edu/pdfs/FranckColonius2009.pdf},
  doi = {https://doi.org/10.2514/6.2009-4019}
}
Freund, J.B. and Colonius, T. Turbulence and sound-field POD analysis of a turbulent jet 2009 International Journal of Aeroacoustics
Vol. 8(4), pp. 337-354 
DOI URL 
Abstract: A Proper Orthogonal Decomposition (POD) is constructed for a Mach 0.9 turbulent jet using a well-validated direct numerical simulation database. Norms are defined based on near-field volume integrals of pressure, turbulence kinetic energy, streamwise velocity, and total enthalpy, two-dimensional integrals of streamswise velocity (to match experimental measurements), and far-field integrals of pressure over a sphere. We find substantially different POD modes for the different norms, and their efficiency at representing the full data is strongly dependent upon the norm and specifically which data we attempt to represent. To reproduce near-field turbulence statistics requires relatively few modes computed by a kinetic energy or pressure norm. However, a large number of the POD modes computed using a near-field norm are required to represent the sound field. The dominant near-field POD modes computed with either the near-field pressure norm or the sound field norm have the structure of wave packets.
BibTeX:
@article{FreundColonius2009,
  author = {Freund, J. B. and Colonius, T.},
  title = {Turbulence and sound-field POD analysis of a turbulent jet},
  journal = {International Journal of Aeroacoustics},
  year = {2009},
  volume = {8},
  number = {4},
  pages = {337-354},
  url = {http://colonius.caltech.edu/pdfs/FreundColonius2009.pdf},
  doi = {https://doi.org/10.1260/147547209787548903}
}
Guðmundsson, K. and Colonius, T. Parabolized Stability Equation Models for Turbulent Jets and Their Radiated Sound 2009 15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference)  DOI URL 
BibTeX:
@inproceedings{GuhmundssonColonius2009,
  author = {Guðmundsson, Kristján and Colonius, Tim},
  title = {Parabolized Stability Equation Models for Turbulent Jets and Their Radiated Sound},
  booktitle = {15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference)},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2009},
  url = {http://colonius.caltech.edu/pdfs/GuhmundssonColonius2009.pdf},
  doi = {https://doi.org/10.2514/6.2009-3380}
}
Joe, W.T., Colonius, T. and MacMynowski, D. Optimized Control of Vortex Shedding From an Inclined Flat Plate 2009 39th AIAA Fluid Dynamics Conference  DOI URL 
BibTeX:
@inproceedings{JoeColoniusMacMynowski2009,
  author = {Joe, Won Tae and Colonius, Tim and MacMynowski, Douglas},
  title = {Optimized Control of Vortex Shedding From an Inclined Flat Plate},
  booktitle = {39th AIAA Fluid Dynamics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2009},
  url = {http://colonius.caltech.edu/pdfs/JoeColoniusMacMynowski2009.pdf},
  doi = {https://doi.org/10.2514/6.2009-4027}
}
Johnsen, E. and Colonius, T. Numerical simulations of non-spherical bubble collapse 2009 Journal of Fluid Mechanics
Vol. 629, pp. 231-262 
DOI URL 
Abstract: A high-order accurate shock- and interface-capturing scheme is used to simulate the collapse of a gas bubble in water. In order to better understand the damage caused by collapsing bubbles, the dynamics of the shock-induced and Rayleigh collapse of a bubble near a planar rigid Surface and in a free field are analysed. Collapse times, bubble displacements, interfacial velocities and surface pressures are quantified as a function of the pressure ratio driving the collapse and of the initial bubble stand-off distance from the wall; these quantities are compared to the available theory and experiments and show good agreement with the data for both the bubble dynamics and the propagation of the shock emitted upon the collapse. Non-spherical collapse involves the formation of a re-entrant jet directed towards the wall or in the direction of propagation of the incoming shock. In shock-induced collapse, very high jet velocities can be achieved, and the finite time for shock propagation through the bubble may be non-negligible compared to the collapse time for the pressure ratios of interest. Several types of shock waves are generated during the collapse, including precursor and water-hammer shocks that arise from the re-entrant jet formation and its impact upon the distal side of the bubble, respectively. The water-hammer shock can generate very high pressures on the wall, far exceeding those from the incident shock. The potential damage to the neighbouring Surface Is quantified by measuring the wall pressure. The range of stand-off distances and the surface area for which amplification of the incident shock due to bubble collapse Occurs is determined.
BibTeX:
@article{JohnsenColonius2009,
  author = {Johnsen, E. and Colonius, T.},
  title = {Numerical simulations of non-spherical bubble collapse},
  journal = {Journal of Fluid Mechanics},
  year = {2009},
  volume = {629},
  pages = {231-262},
  url = {http://colonius.caltech.edu/pdfs/JohnsenColonius2009.pdf},
  doi = {https://doi.org/10.1017/S0022112009006351}
}
Johnsen, E., Colonius, T. and Cleveland, R. Damage potential of the shock-induced collapse of a gas bubble 2009 CAV2009: Seventh International Symposium on Cavitation, Ann Arbor, MI  URL 
BibTeX:
@inproceedings{JohnsenColoniusCleveland2009,
  author = {Johnsen, E. and Colonius, T. and Cleveland, R.O.},
  title = {Damage potential of the shock-induced collapse of a gas bubble},
  booktitle = {CAV2009: Seventh International Symposium on Cavitation, Ann Arbor, MI},
  year = {2009},
  url = {http://colonius.caltech.edu/pdfs/JohnsenColoniusCleveland2009.pdf}
}
Krimmel, J. and Colonius, T. In vivo simulation of shock wave lithotripsy: Wave focusing in inhomogeneous materials 2009 157th Meeting of the Acoustical Society of America  DOI  
BibTeX:
@inproceedings{KrimmelColonius2009,
  author = {Krimmel, Jeffrey and Colonius, Tim},
  title = {In vivo simulation of shock wave lithotripsy: Wave focusing in inhomogeneous materials},
  booktitle = {157th Meeting of the Acoustical Society of America},
  year = {2009},
  doi = {https://doi.org/10.1121/1.4783996}
}
Ran, H.Y. and Colonius, T. Numerical simulation of the sound radiated by a turbulent vortex ring 2009 International Journal of Aeroacoustics
Vol. 8(4), pp. 317-336 
DOI URL 
Abstract: The acoustic field radiated by a turbulent vortex ring is studied. Direct Numerical Simulations (DNS) of the fully compressible, three-dimensional Navier-Stokes equations are used to generate an axisymmetric vortex ring to which 3D stochastic disturbances are added. The disturbances cause instability and turbulent transition of the vortex ring. Detailed information about temporal evolution of sound pressure level, spectrum and directivity associated with modes of oscillation and their turbulent breakdown are investigated. The peak frequency agrees well with experiments, and the modal directivities agree well with predictions of vortex sound theory. Based on the self-similar decay of the turbulent near field, the self-similar decay of the sound field is investigated. We also explore the connections with jet noise by modeling the jet as a de-correlated train of vortex rings.
BibTeX:
@article{RanColonius2009,
  author = {Ran, H. Y. and Colonius, T.},
  title = {Numerical simulation of the sound radiated by a turbulent vortex ring},
  journal = {International Journal of Aeroacoustics},
  year = {2009},
  volume = {8},
  number = {4},
  pages = {317-336},
  url = {http://colonius.caltech.edu/pdfs/RanColonius2009.pdf},
  doi = {https://doi.org/10.2514/6.2004-2918}
}
Schlinker, R., Simonich, J., Shannon, D., Reba, R., Colonius, T., Gudmundsson, K. and Ladeinde, F. Supersonic Jet Noise from Round and Chevron Nozzles: Experimental Studies 2009 15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference)  DOI URL 
BibTeX:
@inproceedings{SchlinkerSimonichShannonEtAl2009,
  author = {Schlinker, Robert and Simonich, John and Shannon, Dan and Reba, Ramons and Colonius, Tim and Gudmundsson, Kristján and Ladeinde, Foluso},
  title = {Supersonic Jet Noise from Round and Chevron Nozzles: Experimental Studies},
  booktitle = {15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference)},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2009},
  url = {http://colonius.caltech.edu/pdfs/SchlinkerSimonichShannonEtAl2009.pdf},
  doi = {https://doi.org/10.2514/6.2009-3257}
}
Schlinker, R.H., Reba, R.A., Simonich, J.C., Colonius, T., Guðmundsson, K. and Ladeinde, F. Towards Prediction and Control of Large Scale Turbulent Structure Supersonic Jet Noise 2009 Proceedings of the Asme Turbo Expo 2009, Vol 1, pp. 217-229  DOI URL 
Abstract: In this paper, we report on progress towards developing physics-based models of sound generation by large-scale turbulent structures in supersonic jet shear layers generally accepted to be the source of aft-angle noise. Aside from obtaining better engineering prediction schemes, the development and optimization of long term jet noise reduction strategies based on controlling instability wave generated large-scale turbulence structures in the shear layer can be more successful if based on predictive flow-noise models, rather than on build and test approaches alone. Such models, if successful, may also provide a path by which laboratory scale demonstrations can be more reliably translated to engine scale. Results show that the noise radiated by large-scale structures in turbulent jet shear layers may be modeled using a RANS based PSE method and projected to the far-field using a Kirchhoff surface approach. A key enabler in this procedure is the development of near-field microphone arrays capable of providing the pressure statistics needed to validate the instability wave models. Our framework provides, for the first time, a deterministic model that will allow understanding and predicting noise radiated by large-scale turbulence.
BibTeX:
@inproceedings{SchlinkerRebaSimonichEtAl2009,
  author = {Schlinker, R. H. and Reba, R. A. and Simonich, J. C. and Colonius, T. and Guðmundsson, K. and Ladeinde, F.},
  title = {Towards Prediction and Control of Large Scale Turbulent Structure Supersonic Jet Noise},
  booktitle = {Proceedings of the Asme Turbo Expo 2009, Vol 1},
  year = {2009},
  pages = {217-229},
  url = {http://colonius.caltech.edu/pdfs/SchlinkerRebaSimonichEtAl2009.pdf},
  doi = {https://doi.org/10.1115/gt2009-60300}
}
Taira, K. and Colonius, T. Effect of Tip Vortices in Low-Reynolds-Number Poststall Flow Control 2009 AIAA Journal
Vol. 47(3), pp. 749-756 
DOI URL 
Abstract: We numerically investigate the application of steady blowing to three-dimensional stalled flows around low-aspect-ratio rectangular flat-plate wings at a Reynolds number of 300. The objective of this study is to explore techniques to enhance lift by directly modifying the dynamics of the wake vortices. Out of various combinations of forcing location and direction considered, we identify two configurations that provide significant lift enhancement. In these cases, actuation appears to strengthen the tip vortices for increased downward induced velocity upon the leading-edge vortices. This in turn moves the low-pressure core directly above the top surface of the wing to greatly enhance lift.
BibTeX:
@article{TairaColonius2009a,
  author = {Taira, K. and Colonius, T.},
  title = {Effect of Tip Vortices in Low-Reynolds-Number Poststall Flow Control},
  journal = {AIAA Journal},
  year = {2009},
  volume = {47},
  number = {3},
  pages = {749-756},
  url = {http://colonius.caltech.edu/pdfs/TairaColonius2009a.pdf},
  doi = {https://doi.org/10.2514/1.40615}
}
Taira, K. and Colonius, T. On the Effect of Tip Vortices in Low-Reynolds-Number Post-Stall Flow Control 2009 47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aerospace Exposition  DOI URL 
BibTeX:
@inproceedings{TairaColonius2009b,
  author = {Taira, Kunihiko and Colonius, Tim},
  title = {On the Effect of Tip Vortices in Low-Reynolds-Number Post-Stall Flow Control},
  booktitle = {47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aerospace Exposition},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2009},
  url = {http://colonius.caltech.edu/pdfs/TairaColonius2009b.pdf},
  doi = {https://doi.org/10.2514/6.2009-376}
}
Taira, K. and Colonius, T. Three-dimensional flows around low-aspect-ratio flat-plate wings at low Reynolds numbers 2009
Vol. 623, pp. 187-207 
DOI URL 
Abstract: Three-dimensional flows over impulsively translated low-aspect-ratio flat plates are investigated for Reynolds numbers of 300 and 500, with a focus on the unsteady vortex dynamics at post-stall angles of attack. Numerical simulations, validated by an oil tow-tank experiment, are performed to study the influence of aspect ratio, angle of attack and planform geometry on the wake vortices and the resulting forces on the plate. Immediately following the impulsive start, the separated flows create wake vortices that share the same topology for all aspect ratios. At large time, the tip vortices significantly influence the vortex dynamics and the corresponding forces on the wings. Depending on the aspect ratio, angle of attack and Reynolds number, the flow at large time reaches a stable steady state, a periodic cycle or aperiodic shedding. For cases of high angles of attack, an asymmetric wake develops in the spanwise direction at large time. The present results are compared to higher Reynolds number flows. Some non-rectangular planforms are also considered to examine the difference in the wakes and forces. After the impulsive start, the time at which maximum lift occurs is fairly constant for a wide range of flow conditions during the initial transient. Due to the influence of the tip vortices, the three-dimensional dynamics of the wake vortices are found to be quite different from the two-dimensional von Karman vortex street in terms of stability and shedding frequency.
BibTeX:
@article{TairaColonius2009,
  author = {Taira, K. and Colonius, T.},
  title = {Three-dimensional flows around low-aspect-ratio flat-plate wings at low Reynolds numbers},
  year = {2009},
  volume = {623},
  pages = {187-207},
  url = {http://colonius.caltech.edu/pdfs/TairaColonius2009.pdf},
  doi = {https://doi.org/10.1017/S0022112008005314}
}
Williams, D., Quach, V., Kerstens, W., Buntain, S., Tadmor, G., Rowley, C. and Colonius, T. Low Reynolds Number Wing Response to an Oscillating Freestream With and Without Feed Forward Control 2009 47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aerospace Exposition  DOI URL 
BibTeX:
@inproceedings{WilliamsQuachKerstensEtAl2009,
  author = {Williams, David and Quach, Vien and Kerstens, Wesley and Buntain, Seth and Tadmor, Gilead and Rowley, Clarence and Colonius, Tim},
  title = {Low Reynolds Number Wing Response to an Oscillating Freestream With and Without Feed Forward Control},
  booktitle = {47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aerospace Exposition},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2009},
  url = {http://colonius.caltech.edu/pdfs/WilliamsQuachKerstensEtAl2009.pdf},
  doi = {https://doi.org/10.2514/6.2009-143}
}
Williams, D.R., Tadmor, G., Colonius, T., Kerstens, W., Quach, V. and Buntain, S. Lift Response of a Stalled Wing to Pulsatile Disturbances 2009 AIAA Journal
Vol. 47(12), pp. 3031-3037 
DOI URL 
Abstract: The transient lift response of a low-Reynolds-number wing subjected to small amplitude pulsatile disturbances is investigated. The wing has a small aspect ratio and a semicircular planform, and it is fully stalled at a 20 deg angle of attack. Microvalve actuators distributed along the leading edge of the wing produce the transient disturbance. It is shown that the lift response to a single pulse increases with increasing actuator supply pressure and that the lift response curves are similar to each other when scaled by the total impulse. Furthermore, for fixed actuator supply pressure, the amplitude and total impulse of the transient lift response curve increases with increasing external flow speed. In this case, the lift response curves are similar when scaled by the dynamic pressure. The lift response to a single pulse can be treated as a filter kernel, and it can be used to predict the lift time history for the arbitrary actuator input signals. The kernel is similar in shape to transient measurements obtained by other investigators on two-dimensional wings and flaps. Comparisons between the model predictions and the experiments using multiple pulse inputs and square-wave modulated input signals at low frequencies are presented.
BibTeX:
@article{WilliamsTadmorColoniusEtAl2009,
  author = {Williams, D. R. and Tadmor, G. and Colonius, T. and Kerstens, W. and Quach, V. and Buntain, S.},
  title = {Lift Response of a Stalled Wing to Pulsatile Disturbances},
  journal = {AIAA Journal},
  year = {2009},
  volume = {47},
  number = {12},
  pages = {3031-3037},
  url = {http://colonius.caltech.edu/pdfs/WilliamsTadmorColoniusEtAl2009.pdf},
  doi = {https://doi.org/10.2514/1.45407}
}
Brès, G.A. and Colonius, T. Three-dimensional instabilities in compressible flow over open cavities 2008 Journal of Fluid Mechanics
Vol. 599, pp. 309-339 
DOI URL 
Abstract: Direct numerical simulations are performed to investigate the three-dimensional stability of compressible flow over open cavities. A linear stability analysis is conducted to search for three-dimensional global instabilities of the two-dimensional mean flow for cavities that are homogeneous in the spanwise direction. The presence of such instabilities is reported for a range of flow conditions and cavity aspect ratios. For cavities of aspect ratio (length to depth) of 2 and 4, the three-dimensional mode has a spanwise wavelength of approximately one cavity depth and oscillates with a frequency about one order of magnitude lower than two-dimensional Rossiter (flow/acoustics) instabilities. A steady mode of smaller spanwise wavelength is also identified for square cavities. The linear results indicate that the instability is hydrodynamic (rather than acoustic) in nature and arises from a generic centrifugal instability mechanism associated with the mean recirculating vortical flow in the downstream part of the cavity. These three-dimensional instabilities are related to centrifugal instabilities previously reported in flows over backward-facing steps, lid-driven cavity flows and Couette flows. Results from three-dimensional simulations of the nonlinear compressible Navier-Stokes equations are also reported. The formation of oscillating (and, in some cases, steady) spanwise structures is observed inside the cavity. The spanwise wavelength and oscillation frequency of these structures agree with the linear analysis predictions. When present, the shear-layer (Rossiter) oscillations experience a low-frequency modulation that arises from nonlinear interactions with the three-dimensional mode. The results are consistent with observations of low-frequency modulations and spanwise structures in previous experimental and numerical studies on open cavity flows.
BibTeX:
@article{BresColonius2008,
  author = {Brès, G. A. and Colonius, T.},
  title = {Three-dimensional instabilities in compressible flow over open cavities},
  journal = {Journal of Fluid Mechanics},
  year = {2008},
  volume = {599},
  pages = {309-339},
  url = {http://colonius.caltech.edu/pdfs/BresColonius2008.pdf},
  doi = {https://doi.org/10.1017/S0022112007009925}
}
Brès, G., Colonius, T. and Fedorov, A. Interaction of Acoustic Disturbances with Micro-Cavities for Ultrasonic Absorptive Coatings 2008 5th AIAA Theoretical Fluid Mechanics Conference  DOI URL 
BibTeX:
@inproceedings{BresColoniusFedorov2008,
  author = {Brès, Guillaume and Colonius, Tim and Fedorov, Alexander},
  title = {Interaction of Acoustic Disturbances with Micro-Cavities for Ultrasonic Absorptive Coatings},
  booktitle = {5th AIAA Theoretical Fluid Mechanics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2008},
  url = {http://colonius.caltech.edu/pdfs/BresColoniusFedorov2008.pdf},
  doi = {https://doi.org/10.2514/6.2008-3903}
}
Brès, G., Colonius, T. and Fedorov, A. Stability of Temporally Evolving Supersonic Boundary Layers over Micro-Cavities for Ultrasonic Absorptive Coatings 2008 5th AIAA Theoretical Fluid Mechanics Conference  DOI URL 
BibTeX:
@inproceedings{BresColoniusFedorov2008a,
  author = {Brès, Guillaume and Colonius, Tim and Fedorov, Alexander},
  title = {Stability of Temporally Evolving Supersonic Boundary Layers over Micro-Cavities for Ultrasonic Absorptive Coatings},
  booktitle = {5th AIAA Theoretical Fluid Mechanics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2008},
  url = {http://colonius.caltech.edu/pdfs/BresColoniusFedorov2008a.pdf},
  doi = {https://doi.org/10.2514/6.2008-4337}
}
Brunton, S., Rowley, C., Taira, K., Colonius, T., Collins, J. and Williams, D. Unsteady Aerodynamic Forces on Small-Scale Wings: Experiments, Simulations, and Models 2008 46th AIAA Aerospace Sciences Meeting and Exhibit  DOI URL 
BibTeX:
@inproceedings{BruntonRowleyTairaEtAl2008,
  author = {Brunton, Steven and Rowley, Clarence and Taira, Kunihiko and Colonius, Tim and Collins, Jesse and Williams, David},
  title = {Unsteady Aerodynamic Forces on Small-Scale Wings: Experiments, Simulations, and Models},
  booktitle = {46th AIAA Aerospace Sciences Meeting and Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2008},
  url = {http://colonius.caltech.edu/pdfs/BruntonRowleyTairaEtAl2008.pdf},
  doi = {https://doi.org/10.2514/6.2008-520}
}
Colonius, T., Hagmeijer, R., Ando, K. and Brennen, C.E. Statistical equilibrium of bubble oscillations in dilute bubbly flows 2008 Physics of Fluids
Vol. 20(4) 
DOI URL 
Abstract: The problem of predicting the moments of the distribution of bubble radius in bubbly flows is considered. The particular case where bubble oscillations occur due to a rapid (impulsive or step change) change in pressure is analyzed, and it is mathematically shown that in this case, inviscid bubble oscillations reach a stationary statistical equilibrium, whereby phase cancellations among bubbles with different sizes lead to time-invariant values of the statistics. It is also shown that at statistical equilibrium, moments of the bubble radius may be computed using the period-averaged bubble radius in place of the instantaneous one. For sufficiently broad distributions of bubble equilibrium (or initial) radius, it is demonstrated that bubble statistics reach equilibrium on a time scale that is fast compared to physical damping of bubble oscillations due to viscosity, heat transfer, and liquid compressibility. The period-averaged bubble radius may then be used to predict the slow changes in the moments caused by the damping. A benefit is that period averaging gives a much smoother integrand, and accurate statistics can be obtained by tracking as few as five bubbles from the broad distribution. The period-averaged formula may therefore prove useful in reducing computational effort in models of dilute bubbly flow wherein bubbles are forced by shock waves or other rapid pressure changes, for which, at present, the strong effects caused by a distribution in bubble size can only be accurately predicted by tracking thousands of bubbles. Some challenges associated with extending the results to more general (nonimpulsive) forcing and strong two-way coupled bubbly flows are briefly discussed.
BibTeX:
@article{ColoniusHagmeijerAndoEtAl2008,
  author = {Colonius, T. and Hagmeijer, R. and Ando, K. and Brennen, C. E.},
  title = {Statistical equilibrium of bubble oscillations in dilute bubbly flows},
  journal = {Physics of Fluids},
  year = {2008},
  volume = {20},
  number = {4},
  url = {http://colonius.caltech.edu/pdfs/ColoniusHagmeijerAndoEtAl2008.pdf},
  doi = {https://doi.org/10.1063/1.2912517}
}
Colonius, T. and Taira, K. A fast immersed boundary method using a nullspace approach and multi-domain far-field boundary conditions 2008 Computer Methods in Applied Mechanics and Engineering
Vol. 197(25-28), pp. 2131-2146 
DOI URL 
Abstract: We report on the continued development of a projection approach for implementing the immersed boundary method for incompressible flows in two and three dimensions. Boundary forces and pressure are regarded as Lagrange multipliers that enable the no-slip and divergence-free constraints to be implicitly determined to arbitrary precision with no associated time-step restrictions. In order to accelerate the method, we further implement a nullspace (discrete streamfunction) method that allows the divergence-free constraint to be automatically satisfied to machine roundoff. By employing a fast sine transform technique, the linear system to determine the forces can be solved efficiently with direct or iterative techniques. A multi-domain technique is developed in order to improve far-field boundary conditions that are compatible with the fast sine transform and account for the extensive potential flow induced by the body as well as vorticity that advects/difluses to large distance from the body. The multi-domain and fast techniques are validated by comparing to the exact solutions for the potential flow induced by stationary and propagating Oseen vortices and by an impulsively-started circular cylinder. Speed-ups of more than an order-of-magnitude are achieved with the new method.
BibTeX:
@article{ColoniusTaira2008,
  author = {Colonius, T. and Taira, K.},
  title = {A fast immersed boundary method using a nullspace approach and multi-domain far-field boundary conditions},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  year = {2008},
  volume = {197},
  number = {25-28},
  pages = {2131-2146},
  url = {http://colonius.caltech.edu/pdfs/ColoniusTaira2008.pdf},
  doi = {https://doi.org/10.1016/j.cma.2007.08.014}
}
Franck, J. and Colonius, T. Large-Eddy Simulation of Separation Control for Compressible Flow Over a Wall-Mounted Hump 2008 46th AIAA Aerospace Sciences Meeting and Exhibit  DOI URL 
BibTeX:
@inproceedings{FranckColonius2008,
  author = {Franck, Jennifer and Colonius, Tim},
  title = {Large-Eddy Simulation of Separation Control for Compressible Flow Over a Wall-Mounted Hump},
  booktitle = {46th AIAA Aerospace Sciences Meeting and Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2008},
  url = {http://colonius.caltech.edu/pdfs/FranckColonius2008.pdf},
  doi = {https://doi.org/10.2514/6.2008-555}
}
Joe, W.T., Taira, K., Colonius, T., MacMynowski, D. and Tadmor, G. Closed-Loop Control of Vortex Shedding on a Two-Dimensional Flat-Plate Airfoil at a Low Reynolds Number 2008 46th AIAA Aerospace Sciences Meeting and Exhibit  DOI URL 
BibTeX:
@inproceedings{JoeTairaColoniusEtAl2008,
  author = {Joe, Won Tae and Taira, Kunihiko and Colonius, Tim and MacMynowski, Douglas and Tadmor, Gilead},
  title = {Closed-Loop Control of Vortex Shedding on a Two-Dimensional Flat-Plate Airfoil at a Low Reynolds Number},
  booktitle = {46th AIAA Aerospace Sciences Meeting and Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2008},
  url = {http://colonius.caltech.edu/pdfs/JoeTairaColoniusEtAl2008.pdf},
  doi = {https://doi.org/10.2514/6.2008-634}
}
Johnsen, E. Numerical simulations of non-spherical bubble collapse with applications to shockwave lithotripsy 2008 School: California Institute of Technology  URL 
Abstract: Shockwave lithotripsy (SWL) is a non-invasive medical procedure in which shockwaves are focused on kidney stones in an attempt to break them. Because the stones are usually immersed in liquid, cavitation occurs during the process. However, the stone comminution mechanisms and the bubble dynamics of SWL are not fully understood. In the present thesis, numerical simulations are employed to study axisymmetric Rayleigh collapse and shock-induced collapse of a single gas bubble in a free field and near a wall. A high-order accurate, quasi-conservative, shock- and interface-capturing scheme is developed to solve the multicomponent Euler equations.

The primary contributions of the present work are the development of a new numerical framework to study compressible multicomponent flows, the characterization of the dynamics of non-spherical bubble collapse, and quantitative measurements of wall pressures generated by bubble collapse. Because of asymmetries in the flow field, a re-entrant jet develops and generates a large water-hammer pressure upon impact onto the distal side. Jet properties are calculated and, as an indication of potential damage, wall pressures are measured; pressures on the order of 1 GPa are achieved locally. In shock-induced collapse, the wall pressure is amplified by the presence of bubbles within several initial radii from the wall. Thus, the pressure generated by the bubble collapse is larger than the incoming shock. The results extended to SWL show that shock-induced collapse has tremendous potential for damage along the stone surface. Furthermore, the simulations are coupled to an elastic wave propagation code to show that bubble collapse may cause damage within kidney stones as well.

BibTeX:
@phdthesis{Johnsen2008,
  author = {Johnsen, Eric},
  title = {Numerical simulations of non-spherical bubble collapse with applications to shockwave lithotripsy},
  school = {California Institute of Technology},
  year = {2008},
  url = {http://resolver.caltech.edu/CaltechETD:etd-05092008-171346}
}
Johnsen, E. and Colonius, T. Damage potential of single‐bubble collapse in shockwave lithotripsy 2008
Vol. 123(5)Acoustics ‘08 Paris, France, pp. 3368-3368 
DOI  
BibTeX:
@inproceedings{JohnsenColonius2008a,
  author = {Johnsen, Eric and Colonius, Tim},
  title = {Damage potential of single‐bubble collapse in shockwave lithotripsy},
  booktitle = {Acoustics ‘08 Paris, France},
  year = {2008},
  volume = {123},
  number = {5},
  pages = {3368-3368},
  doi = {https://doi.org/10.1121/1.2933980}
}
Johnsen, E. and Colonius, T. Shock-induced collapse of a gas bubble in shockwave lithotripsy 2008 Journal of the Acoustical Society of America
Vol. 124(4), pp. 2011-2020 
DOI URL 
Abstract: The shock-induced collapse of a pre-existing nucleus near a solid surface in the focal region of a lithotripter is investigated. The entire flow field of the collapse of a single gas bubble subjected to a lithotripter pulse is simulated using a high-order accurate shock- and interface-capturing scheme, and the wall pressure is considered as an indication of potential damage. Results from the computations show the same qualitative behavior as that observed in experiments: a re-entrant jet forms in the direction of propagation of the pulse and penetrates the bubble during collapse, ultimately hitting the distal side and generating a water-hammer shock. As a result of the propagation of this wave, wall pressures on the order of I GPa may be achieved for bubbles collapsing close to the wall. The wall pressure decreases with initial stand-off distance and pulse width and increases with pulse amplitude. For the stand-off distances considered in the present work, the wall pressure due to bubble collapse is larger than that due to the incoming shockwave; the region over which this holds may extend to ten initial radii. The present results indicate that shock-induced collapse is a mechanism with high potential for damage in shockwave lithotripsy.
BibTeX:
@article{JohnsenColonius2008,
  author = {Johnsen, E. and Colonius, T.},
  title = {Shock-induced collapse of a gas bubble in shockwave lithotripsy},
  journal = {Journal of the Acoustical Society of America},
  year = {2008},
  volume = {124},
  number = {4},
  pages = {2011-2020},
  url = {http://colonius.caltech.edu/pdfs/JohnsenColonius2008.pdf},
  doi = {https://doi.org/10.1121/1.2973229}
}
Krimmel, J. and Colonius, T. Numerical simulation of shock wave generation and focusing in shock wave lithotripsy 2008 Acoustics '08, Paris, France  DOI  
BibTeX:
@inproceedings{KrimmelColonius2008,
  author = {Krimmel, Jeffrey and Colonius, Tim},
  title = {Numerical simulation of shock wave generation and focusing in shock wave lithotripsy},
  booktitle = {Acoustics '08, Paris, France},
  year = {2008},
  doi = {https://doi.org/10.1121/1.2933977}
}
Munson, M., Dickson, W., Colonius, T. and Gharib, M. A New Low Reynolds Number Facility for Active Flow Control Applications 2008 46th AIAA Aerospace Sciences Meeting and Exhibit  DOI URL 
BibTeX:
@inproceedings{MunsonDicksonColoniusEtAl2008,
  author = {Munson, Matthew and Dickson, William and Colonius, Tim and Gharib, Morteza},
  title = {A New Low Reynolds Number Facility for Active Flow Control Applications},
  booktitle = {46th AIAA Aerospace Sciences Meeting and Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2008},
  url = {http://colonius.caltech.edu/pdfs/MunsonDicksonColoniusEtAl2008.pdf},
  doi = {https://doi.org/10.2514/6.2008-694}
}
Rowley, C., Ahuja, S., Taira, K. and Colonius, T. Closed-Loop Control of Leading Edge Vorticity on a 3D Wing: Simulations and Low-Dimensional Models 2008 38th Fluid Dynamics Conference and Exhibit  DOI URL 
BibTeX:
@inproceedings{RowleyAhujaTairaEtAl2008,
  author = {Rowley, Clarence and Ahuja, Sunil and Taira, Kuhiniko and Colonius, Tim},
  title = {Closed-Loop Control of Leading Edge Vorticity on a 3D Wing: Simulations and Low-Dimensional Models},
  booktitle = {38th Fluid Dynamics Conference and Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2008},
  url = {http://colonius.caltech.edu/pdfs/RowleyAhujaTairaEtAl2008.pdf},
  doi = {https://doi.org/10.2514/6.2008-3981}
}
Schlinker, R., Simonich, J., Reba, R., Colonius, T. and Ladeinde, F. Decomposition of High Speed Jet Noise: Source Characteristics and Propagation Effects 2008 14th AIAA/CEAS Aeroacoustics Conference (29th AIAA Aeroacoustics Conference)  DOI URL 
BibTeX:
@inproceedings{SchlinkerSimonichRebaEtAl2008,
  author = {Schlinker, Robert and Simonich, John and Reba, Ramons and Colonius, Tim and Ladeinde, Foluso},
  title = {Decomposition of High Speed Jet Noise: Source Characteristics and Propagation Effects},
  booktitle = {14th AIAA/CEAS Aeroacoustics Conference (29th AIAA Aeroacoustics Conference)},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2008},
  url = {http://colonius.caltech.edu/pdfs/SchlinkerSimonichRebaEtAl2008.pdf},
  doi = {https://doi.org/10.2514/6.2008-2890}
}
Tadmor, G., Bissex, D., Noack, B., Morzynski, M., Colonius, T. and Taira, K. Fast Approximated POD for a Flat Plate Benchmark with a Time Varying Angle of Attack 2008 4th Flow Control Conference  DOI URL 
BibTeX:
@inproceedings{TadmorBissexNoackEtAl2008a,
  author = {Tadmor, Gliead and Bissex, Daniel and Noack, Bernd and Morzynski, Marek and Colonius, Tim and Taira, Kunihiko},
  title = {Fast Approximated POD for a Flat Plate Benchmark with a Time Varying Angle of Attack},
  booktitle = {4th Flow Control Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2008},
  url = {http://colonius.caltech.edu/pdfs/TadmorBissexNoackEtAl2008a.pdf},
  doi = {https://doi.org/10.2514/6.2008-4191}
}
Tadmor, G., Bissex, D., Noack, B., Morzynski, M., Colonius, T. and Taira, K. Temporal-Harmonic Specific POD Mode Extraction 2008 4th Flow Control Conference  DOI URL 
BibTeX:
@inproceedings{TadmorBissexNoackEtAl2008,
  author = {Tadmor, Gliead and Bissex, Daniel and Noack, Bernd and Morzynski, Marek and Colonius, Tim and Taira, Kunihiko},
  title = {Temporal-Harmonic Specific POD Mode Extraction},
  booktitle = {4th Flow Control Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2008},
  url = {http://colonius.caltech.edu/pdfs/TadmorBissexNoackEtAl2008.pdf},
  doi = {https://doi.org/10.2514/6.2008-4190}
}
Tadmor, G., Williams, D., Collins, J., Colonius, T. and Rowley, C. Control of a Semi-Circular Planform Wing in a "Gusting" Unsteady Free stream Flow II: Modeling and Feedback Design 2008 38th Fluid Dynamics Conference and Exhibit  DOI URL 
BibTeX:
@inproceedings{TadmorWilliamsCollinsEtAl2008,
  author = {Tadmor, Gilead and Williams, David and Collins, Jesse and Colonius, Tim and Rowley, Clarence},
  title = {Control of a Semi-Circular Planform Wing in a "Gusting" Unsteady Free stream Flow II: Modeling and Feedback Design},
  booktitle = {38th Fluid Dynamics Conference and Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2008},
  url = {http://colonius.caltech.edu/pdfs/TadmorWilliamsCollinsEtAl2008.pdf},
  doi = {https://doi.org/10.2514/6.2008-3977}
}
Taira, K. The immersed boundary projection method and its application to simulation and control of flows around low-aspect-ratio wings 2008 School: California Institute of Technology  URL 
Abstract: First, we present a new formulation of the immersed boundary method that is algebraically identical to the traditional fractional step algorithm. This method, called the immersed boundary projection method, allows for the simulations of incompressible flows over arbitrarily shaped bodies under motion and/or deformation in both two and three dimensions. The no-slip condition along the immersed boundary is enforced simultaneously with the incompressibility constraint through a single projection. The boundary force is determined implicitly without any constitutive relations for the rigid body formulation, which in turn allows the use of high CFL numbers in our simulations compared to past methods.

Next, the above immersed boundary projection method is used to analyze three-dimensional separated flows around low-aspect-ratio flat-plate wings. A number of simulations highlighting the unsteady nature of the separated flows are performed for Re=300 and 500 with various aspect ratios, angles of attack, and planform geometries. The aspect ratio and angle of attack are found to have a large influence on the stability of the wake profile and the force experienced by the low-aspect-ratio wing. At early times, following an impulsive start, topologies of the wake vortices are found to be the same across different aspect ratios and angles of attack. Behind low-aspect-ratio rectangular plates, leading-edge vortices form and eventually separate as hairpin vortices following the start-up. This phenomenon is found to be similar to dynamic stall observed behind pitching plates. The detached structure would then interact with the tip vortices, reducing the downward velocity induced by the tip vortices acting upon the leading-edge vortex. At large time, depending on the aspect ratio and angles of attack, the wakes reach one of the three states: (i) a steady state, (ii) a periodic unsteady state, or (iii) an aperiodic unsteady state. We have observed that the tip effects in three-dimensional flows can stabilize the flow and also exhibit nonlinear interaction with the shedding vortices.

At last, we apply steady blowing to separated flows behind the low-aspect-ratio rectangular wings. The objective of the flow control is to enhance lift at post-stall angles of attack by changing the dynamics of the wake vortices. This controller strengthens the tip vortices by engulfing the trailing-edge vortex sheet to increase the downward thrust and the downward induced velocity onto the leading-edge vortices. The tip vortices that are traditionally considered as an aerodynamic nuisance, have been used favorably to increase lift in post-stall flows for the considered low-aspect-ratio wings.

BibTeX:
@phdthesis{Taira2008,
  author = {Taira, Kunihiko},
  title = {The immersed boundary projection method and its application to simulation and control of flows around low-aspect-ratio wings},
  school = {California Institute of Technology},
  year = {2008},
  url = {http://resolver.caltech.edu/CaltechETD:etd-05232008-124342}
}
Williams, D., Collins, J., Jankhot, C., Colonius, T. and Tadmor, G. Control of Flow Structure on a Semi-Circular Planform Wing 2008 46th AIAA Aerospace Sciences Meeting and Exhibit  DOI URL 
BibTeX:
@inproceedings{WilliamsCollinsJankhotEtAl2008,
  author = {Williams, David and Collins, Jesse and Jankhot, Crystal and Colonius, Tim and Tadmor, Gilead},
  title = {Control of Flow Structure on a Semi-Circular Planform Wing},
  booktitle = {46th AIAA Aerospace Sciences Meeting and Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2008},
  url = {http://colonius.caltech.edu/pdfs/WilliamsCollinsJankhotEtAl2008.pdf},
  doi = {https://doi.org/10.2514/6.2008-597}
}
Williams, D., Collins, J., Tadmor, G. and Colonius, T. Control of a Semi-Circular Planform Wing in a "Gusting" Unsteady Freestream Flow: I-Experimental Issues 2008 38th Fluid Dynamics Conference and Exhibit  DOI URL 
BibTeX:
@inproceedings{WilliamsCollinsTadmorEtAl2008,
  author = {Williams, David and Collins, Jesse and Tadmor, Gilead and Colonius, Tim},
  title = {Control of a Semi-Circular Planform Wing in a "Gusting" Unsteady Freestream Flow: I-Experimental Issues},
  booktitle = {38th Fluid Dynamics Conference and Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2008},
  url = {http://colonius.caltech.edu/pdfs/WilliamsCollinsTadmorEtAl2008.pdf},
  doi = {https://doi.org/10.2514/6.2008-3976}
}
Ahuja, S., Rowley, C., Kevrekidis, I., Wei, M., Colonius, T. and Tadmor, G. Low-Dimensional Models for Control of Leading-Edge Vortices: Equilibria and Linearized Models 2007 45th AIAA Aerospace Sciences Meeting and Exhibit  DOI URL 
BibTeX:
@inproceedings{AhujaRowleyKevrekidisEtAl2007,
  author = {Ahuja, Sunil and Rowley, Clarence and Kevrekidis, Ioannis and Wei, Mingjun and Colonius, Tim and Tadmor, Gilead},
  title = {Low-Dimensional Models for Control of Leading-Edge Vortices: Equilibria and Linearized Models},
  booktitle = {45th AIAA Aerospace Sciences Meeting and Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2007},
  url = {http://colonius.caltech.edu/pdfs/AhujaRowleyKevrekidisEtAl2007.pdf},
  doi = {https://doi.org/10.2514/6.2007-709}
}
Brès, G. Numerical simulations of three-dimensional instabilities in cavity flows 2007 School: California Institute of Technology  URL 
Abstract: Direct numerical simulations are performed to investigate the stability of compressible flow over three-dimensional open cavities for future control applications.

First, the typical self-sustained oscillations, commonly referred as shear-layer (Rossiter) modes, are characterized for two-dimensional cavities over a range of flow conditions. A linear stability analysis is then conducted to search for three-dimensional global instabilities of the 2D mean flow for cavities that are homogeneous in the spanwise direction. The presence of such instabilities is reported for a range of cavity configurations. For cavities of aspect ratio (length to depth) of 2 and 4, the three-dimensional mode has a spanwise wavelength of approximately 1 cavity depth and oscillates with a frequency about an order-of-magnitude lower than two-dimensional Rossiter (flow/acoustics) instabilities. A steady mode of smaller spanwise wavelength is also identified for square cavities. The linear results indicate that the instability is hydrodynamic (rather than acoustic) in nature and arises from a generic centrifugal instability mechanism associated with the mean recirculating vortical flow in the downstream part of the cavity. These three-dimensional instabilities are related to centrifugal instabilities reported in flows over backward-facing steps, lid-driven cavity flows, and Couette flows.

Results from three-dimensional simulations of the nonlinear compressible Navier-Stokes equations are also reported. The formation of oscillating (and, in some cases, steady) spanwise structures is observed inside the cavity. The spanwise wavelength and oscillation frequency of these structures agree with the linear analysis predictions. When present, the shear-layer (Rossiter) oscillations experience a low-frequency modulation that arises from nonlinear interactions with the three-dimensional mode. These results are consistent with observations of low-frequency modulations and spanwise structures in previous experimental and numerical studies on open cavity flows.

BibTeX:
@phdthesis{Bres2007,
  author = {Brès, Guillaume},
  title = {Numerical simulations of three-dimensional instabilities in cavity flows},
  school = {California Institute of Technology},
  year = {2007},
  url = {http://resolver.caltech.edu/CaltechETD:etd-04262007-095945}
}
Brès, G. and Colonius, T. Direct Numerical Simulations of Three-Dimensional Cavity Flows 2007 13th AIAA/CEAS Aeroacoustics Conference (28th AIAA Aeroacoustics Conference)  DOI URL 
BibTeX:
@inproceedings{BresColonius2007a,
  author = {Brès, Guillaume and Colonius, Tim},
  title = {Direct Numerical Simulations of Three-Dimensional Cavity Flows},
  booktitle = {13th AIAA/CEAS Aeroacoustics Conference (28th AIAA Aeroacoustics Conference)},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2007},
  url = {http://colonius.caltech.edu/pdfs/BresColonius2007a.pdf},
  doi = {https://doi.org/10.2514/6.2007-3405}
}
Brès, G. and Colonius, T. Three-Dimensional Linear Stability Analysis of Cavity Flows 2007 45th AIAA Aerospace Sciences Meeting and Exhibit  DOI URL 
BibTeX:
@inproceedings{BresColonius2007,
  author = {Brès, Guillaume and Colonius, Tim},
  title = {Three-Dimensional Linear Stability Analysis of Cavity Flows},
  booktitle = {45th AIAA Aerospace Sciences Meeting and Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2007},
  url = {http://colonius.caltech.edu/pdfs/BresColonius2007.pdf},
  doi = {https://doi.org/10.2514/6.2007-1126}
}
Freund, J.B., Colonius, T. and Evan, A.P. A cumulative shear mechanism for tissue damage initiation in shock-wave lithotripsy 2007 Ultrasound in Medicine and Biology
Vol. 33(9), pp. 1495-1503 
DOI URL 
Abstract: Evidence suggests that inertial cavitation plays an important role in the renal injury incurred during shock-wave lithotripsy. However, it is unclear how tissue damage is initiated, and significant injury typically occurs only after a sufficient dose of shock waves. Although it has been suggested that shock-induced shearing might initiate injury, estimates indicate that individual shocks do not produce sufficient shear to do so. In this paper, we hypothesize that the cumulative shear of the many shocks is damaging. This mechanism depends on whether there is sufficient time between shocks for tissue to relax to its unstrained state. We investigate the mechanism with a physics-based simulation model, wherein the basement membranes that define the tubules and vessels in the inner medulla are represented as elastic shells surrounded by viscous fluid. Material properties are estimated from in-vitro tests of renal basement membranes and documented mechanical properties of cells and extracellular gels. Estimates for the net shear deformation from a typical lithotripter shock (similar to 0.1 %) are found from a separate dynamic shock simulation. The results suggest that the larger interstitial volume (similar to 40%) near the papilla tip gives the tissue there a relaxation time comparable to clinical shock delivery rates (similar to 1 Hz), thus allowing shear to accumulate. Away from the papilla tip, where the interstitial volume is smaller (similar to 20%), the model tissue relaxes completely before the next shock would be delivered. Implications of the model are that slower delivery rates and broader focal zones should both decrease injury, consistent with some recent observations.
BibTeX:
@article{FreundColoniusEvan2007,
  author = {Freund, J. B. and Colonius, T. and Evan, A. P.},
  title = {A cumulative shear mechanism for tissue damage initiation in shock-wave lithotripsy},
  journal = {Ultrasound in Medicine and Biology},
  year = {2007},
  volume = {33},
  number = {9},
  pages = {1495-1503},
  url = {http://colonius.caltech.edu/pdfs/FreundColoniusEvan2007.pdf},
  doi = {https://doi.org/10.1016/j.ultrasmedbio.2007.03.001}
}
Guðmundsson, K. and Colonius, T. Spatial Stability Analysis of Chevron Jet Profiles 2007 13th AIAA/CEAS Aeroacoustics Conference (28th AIAA Aeroacoustics Conference)  DOI URL 
BibTeX:
@inproceedings{GuhmundssonColonius2007,
  author = {Guðmundsson, Kristján and Colonius, Tim},
  title = {Spatial Stability Analysis of Chevron Jet Profiles},
  booktitle = {13th AIAA/CEAS Aeroacoustics Conference (28th AIAA Aeroacoustics Conference)},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2007},
  url = {http://colonius.caltech.edu/pdfs/GuhmundssonColonius2007.pdf},
  doi = {https://doi.org/10.2514/6.2007-3599}
}
Johnsen, E. and Colonius, T. Numerical study of the collapse of a bubble subjected to a lithotripter pulse 2007
Vol. 900Renal Stone Disease, 1st Annual International Urolithiasis Research Symposium, pp. 360-363 
URL 
Abstract: The collapse of a bubble subjected to a lithotripter pulse is studied numerically. The goal is to record the pressure exerted along the stone, as a measure of potential stone damage. It is found that the pressure due to buble collapse is much larger than that of the lithotripter pulse. Furthermore, the pressure greatly depends on the geometry of the problem (initial stand-off distance and bubble size) and on the properties of the pulse (amplitude and width).
BibTeX:
@inproceedings{JohnsenColonius2007,
  author = {Johnsen, E. and Colonius, T.},
  title = {Numerical study of the collapse of a bubble subjected to a lithotripter pulse},
  booktitle = {Renal Stone Disease, 1st Annual International Urolithiasis Research Symposium},
  year = {2007},
  volume = {900},
  pages = {360-363},
  url = {http://colonius.caltech.edu/pdfs/JohnsenColonius2007.pdf}
}
Johnsen, E., Colonius, T., Kreider, W. and Bailey, M.R. Non-spherical collapse of an air bubble subjected to a lithotripter pulse 2007 Proceedings of the ASME International Mechanical Engineering Congress and Exposition 2007, Vol 2, pp. 285-294  DOI URL 
Abstract: In order to better understand the contribution of bubble collapse to stone comminution in shockwave lithotripsy, the shock-induced and Rayleigh collapse of a spherical air bubble is investigated using numerical simulations, and the free-field collapse of a cavitation bubble is studied experimentally. In shock-induced collapse near a wall, it is found that the presence of the bubble greatly amplifies the pressure recorded at the stone surface; the functional dependence of the wall pressure on the initial standoff distance and the amplitude are presented. In Rayleigh collapse near a solid surface, the proximity of the wall retards the flow and leads to a more prominent jet. Experiments show that re-entrant jets form in the collapse of cavitation bubbles excited by lithotripter shockwaves in a fashion comparable to previous studies of collapse near a solid surface.
BibTeX:
@inproceedings{JohnsenColoniusKreiderEtAl2007,
  author = {Johnsen, E. and Colonius, T. and Kreider, W. and Bailey, M. R.},
  title = {Non-spherical collapse of an air bubble subjected to a lithotripter pulse},
  booktitle = {Proceedings of the ASME International Mechanical Engineering Congress and Exposition 2007, Vol 2},
  year = {2007},
  pages = {285-294},
  url = {http://colonius.caltech.edu/pdfs/JohnsenColoniusKreiderEtAl2007.pdf},
  doi = {https://doi.org/10.1115/imece2007-43156}
}
Preston, A.T., Colonius, T. and Brennen, C.E. A reduced-order model of diffusive effects on the dynamics of bubbles 2007 Physics of Fluids
Vol. 19(12) 
DOI URL 
Abstract: We propose a new reduced-order model for spherical bubble dynamics that accurately captures the effects of heat and mass diffusion. The objective is to reduce the full system of partial differential equations to a set of coupled ordinary differential equations that are efficient enough to implement into complex bubbly flow computations. Comparisons to computations of the full partial differential equations and of other reduced-order models are used to validate the model and establish its range of validity.
BibTeX:
@article{PrestonColoniusBrennen2007,
  author = {Preston, A. T. and Colonius, T. and Brennen, C. E.},
  title = {A reduced-order model of diffusive effects on the dynamics of bubbles},
  journal = {Physics of Fluids},
  year = {2007},
  volume = {19},
  number = {12},
  url = {http://colonius.caltech.edu/pdfs/PrestonColoniusBrennen2007.pdf},
  doi = {https://doi.org/10.1063/1.2825018}
}
Taira, K. and Colonius, T. The immersed boundary method: a projection approach 2007
Vol. 225(2), pp. 2118-2137 
DOI URL 
Abstract: A new formulation of the immersed boundary method with a structure algebraically identical to the traditional fractional step method is presented for incompressible flow over bodies with prescribed surface motion. Like previous methods, a boundary force is applied at the immersed surface to satisfy the no-slip constraint. This extra constraint can be added to the incompressible Navier-Stokes equations by introducing regularization and interpolation operators. The current method gives prominence to the role of the boundary force acting as a Lagrange multiplier to satisfy the no-slip condition. This role is analogous to the effect of pressure on the momentum equation to satisfy the divergence-free constraint. The current immersed boundary method removes slip and non-divergence-free components of the velocity field through a projection. The boundary force is determined implicitly without any constitutive relations allowing the present formulation to use larger CFL numbers compared to some past methods. Symmetry and positive-definiteness of the system are preserved such that the conjugate gradient method can be used to solve for the flow field. Examples show that the current formulation achieves second-order temporal accuracy and better than first-order spatial accuracy in L-2-norms for one- and two-dimensional test problems. Results from two-dimensional simulations of flows over stationary and moving cylinders are in good agreement with those from previous experimental and numerical studies.
BibTeX:
@article{TairaColonius2007,
  author = {Taira, K. and Colonius, T.},
  title = {The immersed boundary method: a projection approach},
  year = {2007},
  volume = {225},
  number = {2},
  pages = {2118-2137},
  url = {http://colonius.caltech.edu/pdfs/TairaColonius2007.pdf},
  doi = {https://doi.org/10.1016/j.jcp.2007.03.005}
}
Taira, K., Dickson, W., Colonius, T., Dickinson, M. and Rowley, C. Unsteadiness in Flow over a Flat Plate at Angle-of-Attack at Low Reynolds Numbers 2007 45th AIAA Aerospace Sciences Meeting and Exhibit  DOI URL 
BibTeX:
@inproceedings{TairaDicksonColoniusEtAl2007,
  author = {Taira, Kunihiko and Dickson, William and Colonius, Tim and Dickinson, Michael and Rowley, Clarence},
  title = {Unsteadiness in Flow over a Flat Plate at Angle-of-Attack at Low Reynolds Numbers},
  booktitle = {45th AIAA Aerospace Sciences Meeting and Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2007},
  url = {http://colonius.caltech.edu/pdfs/TairaDicksonColoniusEtAl2007.pdf},
  doi = {https://doi.org/10.2514/6.2007-710}
}
Williams, D., Doshi, S., Collins, J. and Colonius, T. Control of the Spanwise Distribution of Circulation on NACA 0012 and Flat Plate Wings 2007 45th AIAA Aerospace Sciences Meeting and Exhibit  DOI URL 
BibTeX:
@inproceedings{WilliamsDoshiCollinsEtAl2007,
  author = {Williams, David and Doshi, Sudeep and Collins, Jesse and Colonius, Tim},
  title = {Control of the Spanwise Distribution of Circulation on NACA 0012 and Flat Plate Wings},
  booktitle = {45th AIAA Aerospace Sciences Meeting and Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2007},
  url = {http://colonius.caltech.edu/pdfs/WilliamsDoshiCollinsEtAl2007.pdf},
  doi = {https://doi.org/10.2514/6.2007-1121}
}
Bailey, M., McAteer, J., Pishchalnikov, Y., Hamilton, M. and Colonius, T. Progress in lithotripsy research 2006 Acoustics Today
Vol. 2(2), pp. 18-29 
URL 
BibTeX:
@article{BaileyMcAteerPishchalnikovEtAl2006,
  author = {Bailey, M.R. and McAteer, J.A. and Pishchalnikov, Y.A. and Hamilton, M.F. and Colonius, T.},
  title = {Progress in lithotripsy research},
  journal = {Acoustics Today},
  year = {2006},
  volume = {2},
  number = {2},
  pages = {18-29},
  url = {http://acousticstoday.org/issues/2006AT/Apr2006/#?page=0}
}
Colonius, T. Computational Aeroacoustics 2006 von Karman Institute for Fluid Dynamics Lecture Series 2006-05  URL 
BibTeX:
@inbook{Colonius2006,
  author = {Colonius, T.},
  title = {Computational Aeroacoustics},
  booktitle = {von Karman Institute for Fluid Dynamics Lecture Series 2006-05},
  publisher = {von Karman Institute for Fluid Dynamics},
  year = {2006},
  url = {http://colonius.caltech.edu/pdfs/Colonius2006.pdf}
}
Guðmundsson, K. and Colonius, T. Linear Stability Analysis of Chevron Jet Profiles 2006 Proceedings of the ASME Fluids Engineering Division Summer Conference, Vol 2, pp. 497-504  DOI URL 
Abstract: We investigate the linear stability characteristics of the mean velocity profiles produced by chevron nozzles. We show that chevron instability waves can be decomposed into azimuthal modes analogously to those of round jets. This facilitates a direct comparison of growth rates and mode structure between different nozzles. We find that the three nozzles used in this study share a set of modes, referred to as primary modes. In addition, we find that there exist modes unique to the chevrons nozzles, termed secondary modes. While chevron jets possess a much larger number of unstable modes, the modes with lowest azimuthal structure show strong suppression of growth rates in two different chevron jets. Some preliminary implications on sound generation are discussed.
BibTeX:
@inproceedings{GuhmundssonColonius2006,
  author = {Guðmundsson, K. and Colonius, T.},
  title = {Linear Stability Analysis of Chevron Jet Profiles},
  booktitle = {Proceedings of the ASME Fluids Engineering Division Summer Conference, Vol 2},
  year = {2006},
  pages = {497-504},
  url = {http://colonius.caltech.edu/pdfs/GuhmundssonColonius2006.pdf},
  doi = {https://doi.org/10.1115/fedsm2006-98485}
}
Johnsen, E. and Colonius, T. Compressible multicomponent flow calculations and shock-bubble interaction 2006 CAV2005: Sixth International Symposium on Cavitation, Wageningen, The Netherlands  URL 
BibTeX:
@inproceedings{JohnsenColonius2006b,
  author = {Johnsen, E. and Colonius, T.},
  title = {Compressible multicomponent flow calculations and shock-bubble interaction},
  booktitle = {CAV2005: Sixth International Symposium on Cavitation, Wageningen, The Netherlands},
  year = {2006},
  url = {http://colonius.caltech.edu/pdfs/JohnsenColonius2006b.pdf}
}
Johnsen, E. and Colonius, T. Implementation of WENO schemes in compressible multicomponent flow problems 2006 Journal of Computational Physics
Vol. 219(2), pp. 715-732 
DOI URL 
Abstract: High-order accurate shock-capturing schemes are capable of properly resolving discontinuities with correct wave speeds in single-fluid Riemann problems. However, when different fluids are present, oscillations develop at interfaces. A class of existing interface-capturing methods that suppress these oscillations is based on first- and second-order accurate reconstructions with Roe solvers. In this paper, we extend these methods to high-order accurate WENO schemes and the HLLC approximate Riemann solver. In particular, we show that a finite volume formulation where the appropriately averaged primitive variables are reconstructed leads to the oscillation-free advection of an isolated interface. Furthermore, numerical experiments show no spurious oscillations for problems where shockwaves and interfaces interact. We solve the Euler equations supplemented by a stiffened equation of state to model flows of gas and liquid components. Our method is high-order accurate, quasi-conservative, shock-capturing and interface-capturing; these properties are additionally verified by considering one-dimensional multicomponent Riemann problems and a two-dimensional shock-bubble interaction.
BibTeX:
@article{JohnsenColonius2006,
  author = {Johnsen, E. and Colonius, T.},
  title = {Implementation of WENO schemes in compressible multicomponent flow problems},
  journal = {Journal of Computational Physics},
  year = {2006},
  volume = {219},
  number = {2},
  pages = {715-732},
  url = {http://colonius.caltech.edu/pdfs/JohnsenColonius2006.pdf},
  doi = {https://doi.org/10.1016/j.jcp.2006.04.018}
}
Johnsen, E. and Colonius, T. Numerical study of the collapse of a bubble subjected to a lithotripter pulse 2006
Vol. 120(5)Proc. 4th Joint Meeting: ASA and ASJ, pp. 3065-3065 
DOI  
BibTeX:
@inproceedings{JohnsenColonius2006a,
  author = {Johnsen, Eric and Colonius, Tim},
  title = {Numerical study of the collapse of a bubble subjected to a lithotripter pulse},
  booktitle = {Proc. 4th Joint Meeting: ASA and ASJ},
  year = {2006},
  volume = {120},
  number = {5},
  pages = {3065-3065},
  doi = {https://doi.org/10.1121/1.4787344}
}
Rowley, C.W., Williams, D.R., Colonius, T., Murray, R.M. and Macmynowski, D.G. Linear models for control of cavity flow oscillations 2006 Journal of Fluid Mechanics
Vol. 547, pp. 317-330 
DOI URL 
Abstract: Models for understanding and controlling oscillations in the flow past a rectangular cavity are developed. These models may be used to guide control designs, to understand performance limits of feedback, and to interpret experimental results. Traditionally, cavity oscillations are assumed to be self-sustained: no external disturbances are necessary to maintain the oscillations, and amplitudes are limited by nonlinearities. We present experimental data which suggests that in some regimes, the oscillations may not be self-sustained, but lightly damped: oscillations are sustained by external forcing, such as boundary-layer turbulence. In these regimes, linear models suffice to describe the behaviour, and the final amplitude of oscillations depends on the characteristics of the external disturbances. These linear models are particularly appropriate for describing cavities in which feedback has been used for noise suppression, as the oscillations are small and nonlinearities are less likely to be important. It is shown that increasing the gain too much in such feedback control experiments can lead to a peak-splitting phenomenon, which is explained by the linear models. Fundamental performance limits indicate that peak splitting is likely to occur for narrow-bandwidth actuators and controllers.
BibTeX:
@article{RowleyWilliamsColoniusEtAl2006,
  author = {Rowley, C. W. and Williams, D. R. and Colonius, T. and Murray, R. M. and Macmynowski, D. G.},
  title = {Linear models for control of cavity flow oscillations},
  journal = {Journal of Fluid Mechanics},
  year = {2006},
  volume = {547},
  pages = {317-330},
  url = {http://colonius.caltech.edu/pdfs/RowleyWilliamsColoniusEtAl2006.pdf},
  doi = {https://doi.org/10.1017/S0022112005007299}
}
Suzuki, T. and Colonius, T. Instability waves in a subsonic round jet detected using a near-field phased microphone array 2006 Journal of Fluid Mechanics
Vol. 565, pp. 197-226 
DOI URL 
Abstract: We propose a diagnostic technique to detect instability waves in a subsonic round jet using a phased microphone array. The detection algorithm is analogous to the beam-forming technique, which is typically used with a far-field microphone array to localize noise sources. By replacing the reference solutions used in the conventional beamforming with eigenfunctions from linear stability analysis, the amplitudes of instability waves in the axisymmetric and first two azimuthal modes are inferred. Experimental measurements with particle image velocimetry and a database from direct numerical simulation are incorporated to design a conical array that is placed just outside the mixing layer near the nozzle exit. The proposed diagnostic technique is tested in experiments by checking for consistency of the radial decay, streamwise evolution and phase correlation of hydrodynamic pressure. The results demonstrate that in a statistical sense, the pressure field is consistent with instability waves evolving in the turbulent mean flow from the nozzle exit to the end of the potential core, particularly near the most amplified frequency of each azimuthal mode. We apply this technique to study the effects of jet Mach number and temperature ratio on the azimuthal mode balance and evolution of instability waves. We also compare the results from the beam-forming algorithm with the proper orthogonal decomposition and discuss some implications for jet noise.
BibTeX:
@article{SuzukiColonius2006,
  author = {Suzuki, T. and Colonius, T.},
  title = {Instability waves in a subsonic round jet detected using a near-field phased microphone array},
  journal = {Journal of Fluid Mechanics},
  year = {2006},
  volume = {565},
  pages = {197-226},
  url = {http://colonius.caltech.edu/pdfs/SuzukiColonius2006.pdf},
  doi = {https://doi.org/10.1017/S0022112006001613}
}
Suzuki, T. and Colonius, T. Relation Between Instability Waves and Low-Frequency Jet Noise Investigated with Phased-Microphone Arrays 2006 44th AIAA Aerospace Sciences Meeting and Exhibit  DOI URL 
BibTeX:
@inproceedings{SuzukiColonius2006a,
  author = {Suzuki, Takao and Colonius, Tim},
  title = {Relation Between Instability Waves and Low-Frequency Jet Noise Investigated with Phased-Microphone Arrays},
  booktitle = {44th AIAA Aerospace Sciences Meeting and Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2006},
  url = {http://colonius.caltech.edu/pdfs/SuzukiColonius2006a.pdf},
  doi = {https://doi.org/10.2514/6.2006-622}
}
Ran, H. Numerical Study of the Dynamics and Sound Generation of a Turbulent Vortex Ring 2005 School: California Institute of Technology  URL 
Abstract: In the present study, Direct Numerical Simulations (DNS) of the fully compressible, three-dimensional Navier-Stokes equations are used to generate an axisymmetric vortex ring to which three-dimensional stochastic disturbances are added. The radiated acoustic field is computed directly in the near field, and by solving the wave equation in a spherical coordinate system in the far field.

At high Reynolds number, a vortex ring will undergo an instability to azimuthal waves. The instability produces higher azimuthal modes and induces nonlinear interaction between the modes, and will cause the vortex ring to break down and transition to turbulence. The early stages of the simulation agree well with the linear instability theory. Nonlinear stage of instability, transition, formation of axial flow and streamwise vorticity are analyzed and compared with experimental results. After turbulent transition, the evolution of statistical quantities becomes independent of viscosity and the initial geometry, and the flow become self-similar. The temporal evolution of quantities including total circulation, axial velocity profile, vortex ring displacement and vorticity profile agrees well with the self-similarity law. Turbulent energy spectrum, Reynolds stresses and turbulence production are also presented.

The unsteady vorticity field generates acoustic waves with higher azimuthal modes, each mode with a distinctive spectrum and directivity. The ensemble averaged peak frequency, bandwidth, and the sound pressure level agrees qualitatively with reported experimental results. The directivity of each azimuthal mode is compared with predictions of vortex sound theory. The sound generation consists of three stages. The first is a deterministic stage when linear instability waves emerge and grow and generate relatively weak sound. The second stage is nonlinear interaction and vortex breakdown; at this stage the sound pressure level reaches a peak value. The third stage is the turbulent asymptotic decay of the acoustic field. Based on the self-similar decay of the turbulent near field, the self-similar decay of the sound field is investigated. Connection between the acoustic field and the vortex ring oscillations is also studied with vortex sound theory. Finally, we note some similarities between the sound radiated by a train of de-correlated vortex rings and turbulent jet noise. The sound pressure level, spectrum, and directivity of the train of vortex rings is similar to the sound field from a jet with similar Reynolds number and Mach number.

BibTeX:
@phdthesis{Ran2005,
  author = {Ran, Hongyu},
  title = {Numerical Study of the Dynamics and Sound Generation of a Turbulent Vortex Ring},
  school = {California Institute of Technology},
  year = {2005},
  url = {http://resolver.caltech.edu/CaltechETD:etd-06082004-151101}
}
Reba, R., Narayanan, S., Colonius, T. and Suzuki, T. Modeling Jet Noise from Organized Structures Using Near-Field Hydrodynamic Pressure 2005 11th AIAA/CEAS Aeroacoustics Conference  DOI URL 
BibTeX:
@inproceedings{RebaNarayananColoniusEtAl2005,
  author = {Reba, Ramons and Narayanan, Satish and Colonius, Tim and Suzuki, Takao},
  title = {Modeling Jet Noise from Organized Structures Using Near-Field Hydrodynamic Pressure},
  booktitle = {11th AIAA/CEAS Aeroacoustics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2005},
  url = {http://colonius.caltech.edu/pdfs/RebaNarayananColoniusEtAl2005.pdf},
  doi = {https://doi.org/10.2514/6.2005-3093}
}
Colonius, T. Modeling artificial boundary conditions for compressible flow 2004 Annual Review of Fluid Mechanics
Vol. 36, pp. 315-345 
DOI URL 
Abstract: We review artificial boundary conditions (BCs) for simulation of inflow, outflow, and far-field (radiation) problems, with an emphasis on techniques suitable for compressible turbulent shear flows. BCs based on linearization near the boundary are usually appropriate for inflow and radiation problems. A variety of accurate techniques have been developed for this case, but some robustness and implementation issues remain. At an outflow boundary, the linearized BCs are usually not accurate enough. Various ad hoc models have been proposed for the nonlinear case, including absorbing layers and fringe methods. We discuss these techniques and suggest directions for future modeling efforts.
BibTeX:
@article{Colonius2004,
  author = {Colonius, T.},
  title = {Modeling artificial boundary conditions for compressible flow},
  journal = {Annual Review of Fluid Mechanics},
  year = {2004},
  volume = {36},
  pages = {315-345},
  url = {http://colonius.caltech.edu/pdfs/Colonius2004.pdf},
  doi = {https://doi.org/10.1146/annurev.fluid.36.050802.121930}
}
Colonius, T. and Lele, S.K. Computational aeroacoustics: progress on nonlinear problems of sound generation 2004 Progress in Aerospace Sciences
Vol. 40(6), pp. 345-416 
DOI URL 
Abstract: Computational approaches are being developed to study a range of problems in aeroacoustics. These aeroacoustic problems may be classified based on the physical processes responsible for the sound radiation, and range from linear problems of radiation, refraction, and scattering in known base flows or by solid bodies, to sound generation by turbulence. In this article, we focus mainly on the challenges and successes associated with numerically simulating sound generation by turbulent flows.
We discuss a hierarchy of computational approaches that range from semi-empirical schemes that estimate the noise sources using mean-flow and turbulence statistics, to high-fidelity unsteady flow simulations that resolve the sound generation process by direct application of the fundamental conservation principles. We stress that high-fidelity methods such as Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) have their merits in helping to unravel the flow physics and the mechanisms of sound generation. They also provide rich databases for modeling activities that will ultimately be needed to improve existing predictive capabilities. Spatial and temporal discretization schemes that are well-suited for aeroacoustic calculations are analyzed, including the effects of artificial dispersion and dissipation on uniform and nonuniform grids. We stress the importance of the resolving power of the discretization as well as computational efficiency of the overall scheme. Boundary conditions to treat the flow of disturbances in and out of the computational domain, as well as methods to mimic anechoic domain extension are discussed. Test cases on some benchmark problems are included to provide a realistic assessment of several boundary condition treatments. Finally, highlights of recent progress are given using selected model problems. These include subsonic cavity and jet noise. In the end, the current challenges in aeroacoustic modeling and in simulation algorithms are revisited with a look toward the future developments.
BibTeX:
@article{ColoniusLele2004,
  author = {Colonius, T. and Lele, S. K.},
  title = {Computational aeroacoustics: progress on nonlinear problems of sound generation},
  journal = {Progress in Aerospace Sciences},
  year = {2004},
  volume = {40},
  number = {6},
  pages = {345-416},
  url = {http://colonius.caltech.edu/pdfs/ColoniusLele2004.pdf},
  doi = {https://doi.org/10.1016/j.paerosci.2004.09.001}
}
Colonius, T., Suzuki, T. and MacMartin, D.G. Feedback Control of Vortex Shedding in a Separated Diffuser 2004 XXI ICTAM, Warsaw, Poland  URL 
BibTeX:
@inproceedings{ColoniusSuzukiMacMartin2004,
  author = {Tim Colonius and Takao Suzuki and Douglas G. MacMartin},
  title = {Feedback Control of Vortex Shedding in a Separated Diffuser},
  booktitle = {XXI ICTAM, Warsaw, Poland},
  year = {2004},
  url = {http://colonius.caltech.edu/pdfs/ColoniusSuzukiMacMartin2004.pdf}
}
Colonius, T., Suzuki, T. and MacMartin, D.G. Feedback Control of Vortex Shedding in a Separated Diffuser 2004 XXI ICTAM, Warsaw, Poland  URL 
BibTeX:
@inproceedings{ColoniusSuzukiMacMartin2004,
  author = {Tim Colonius and Takao Suzuki and Douglas G. MacMartin},
  title = {Feedback Control of Vortex Shedding in a Separated Diffuser},
  booktitle = {XXI ICTAM, Warsaw, Poland},
  year = {2004},
  url = {http://colonius.caltech.edu/pdfs/ColoniusSuzukiMacMartin2004.pdf}
}
Preston, A. Modeling heat and mass transfer in bubbly cavitating flows and shock waves in cavitating nozzles 2004 School: California Institute of Technology  URL 
Abstract: Two problems are considered in this thesis: the modeling of heat and mass diffusion effects on the dynamics of spherical bubbles, and the computation of unsteady, bubbly cavitating flows in nozzles. The goal of Part I is to develop a reduced-order model that is able to accurately and efficiently capture the effect of heat and mass transfer on the dynamics of bubbles. Detailed computations of forced and oscillating bubbles including heat and mass diffusion show that the assumptions of polytropic behavior, constant vapor pressure, and an effective liquid viscosity do not accurately account for diffusive damping and thus do not accurately capture bubble dynamics. While the full bubble computations are readily performed for single bubbles, they are too expensive to implement into continuum models of complex bubbly flows where the radial diffusion equations would have to be solved at each grid point. Therefore reduced-order models that accurately capture diffusive effects are needed.

We first develop a full bubble computation, where the full set of radial conservation equations are solved in the bubble interior and surrounding liquid. This provides insight as to which equations, or terms in equations, may be able to be neglected while still accurately capturing the bubble dynamics. Motivated by results of the full computations, we use constant heat and mass transfer coefficients to model the transfer at the bubble wall. In the resulting reduced-order model the heat and mass diffusion equations are each replaced by a single ordinary differential equation. The model is therefore efficient enough to implement into continuum computations. Comparisons of the reduced-order model to the full computations over a wide range of parameters indicate agreement that is superior to existing models.

In Part II we investigate the effects of unsteady bubble dynamics on cavitating flow through a converging-diverging nozzle. A continuum model that couples the Rayleigh-Plesset equation with the continuity and momentum equations is used to formulate unsteady, quasi-one-dimensional partial differential equations. Flow regimes studied include those where steady state solutions exist, and those where steady state solutions diverge at the so-called flashing instability. These latter flows consist of unsteady bubbly shock waves traveling downstream in the diverging section of the nozzle. An approximate analytical expression is developed to predict the critical back pressure for choked flow. The results agree with previous barotropic models for those flows where bubble dynamics are not important, but show that in many instances the neglect of bubble dynamics cannot be justified. Finally the computations show reasonable agreement with an experiment that measures the spatial variation of pressure, velocity and void fraction for steady shock free flows, and good agreement with an experiment that measures the throat pressure and shock position for flows with bubbly shocks. In the model, damping of the bubble radial motion is restricted to a simple "effective" viscosity to account for diffusive effects. However, many features of the nozzle flow are shown to be independent of the specific damping mechanism. This is confirmed by the implementation of the more sophisticated diffusive modeling developed in Part I.

BibTeX:
@phdthesis{Preston2004,
  author = {Preston, Alastair},
  title = {Modeling heat and mass transfer in bubbly cavitating flows and shock waves in cavitating nozzles},
  school = {California Institute of Technology},
  year = {2004},
  url = {http://resolver.caltech.edu/CaltechETD:etd-12182003-150738}
}
Ran, H. and Colonius, T. Numerical Simulation of Sound Radiated from a Turbulent Vortex Ring 2004 10th AIAA/CEAS Aeroacoustics Conference  DOI URL 
BibTeX:
@inproceedings{RanColonius2004,
  author = {Ran, Hongyu and Colonius, Tim},
  title = {Numerical Simulation of Sound Radiated from a Turbulent Vortex Ring},
  booktitle = {10th AIAA/CEAS Aeroacoustics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2004},
  url = {http://colonius.caltech.edu/pdfs/RanColonius2004.pdf},
  doi = {https://doi.org/10.2514/6.2004-2918}
}
Rowley, C.W., Colonius, T. and Murray, R.M. Model reduction for compressible flows using POD and Galerkin projection 2004 Physica D-Nonlinear Phenomena
Vol. 189(1-2), pp. 115-129 
DOI URL 
Abstract: We present a framework for applying the method of proper orthogonal decomposition (POD) and Galerkin projection to compressible fluids. For incompressible flows, only the kinematic variables are important, and the techniques are well known. In a compressible flow, both the kinematic and thermodynamic variables are dynamically important, and must be included in the configuration space. We introduce an energy-based inner product which may be used to obtain POD modes for this configuration space. We then obtain an approximate version of the Navier-Stokes equations, valid for cold flows at moderate Mach number, and project these equations onto a POD basis. The resulting equations of motion are quadratic, and are much simpler than projections of the full compressible Navier-Stokes equations.
BibTeX:
@article{RowleyColoniusMurray2004,
  author = {Rowley, C. W. and Colonius, T. and Murray, R. M.},
  title = {Model reduction for compressible flows using POD and Galerkin projection},
  journal = {Physica D-Nonlinear Phenomena},
  year = {2004},
  volume = {189},
  number = {1-2},
  pages = {115-129},
  url = {http://colonius.caltech.edu/pdfs/RowleyColoniusMurray2004.pdf},
  doi = {https://doi.org/10.1016/j.physd.2003.03.001}
}
Suzuki, T. and Colonius, T. Identification of Jet Instability Waves and Design of a Microphone Array 2004 10th AIAA/CEAS Aeroacoustics Conference  DOI URL 
BibTeX:
@inproceedings{SuzukiColonius2004,
  author = {Suzuki, Takao and Colonius, Tim},
  title = {Identification of Jet Instability Waves and Design of a Microphone Array},
  booktitle = {10th AIAA/CEAS Aeroacoustics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2004},
  url = {http://colonius.caltech.edu/pdfs/SuzukiColonius2004.pdf},
  doi = {https://doi.org/10.2514/6.2004-2960}
}
Suzuki, T., Colonius, T. and MacMartin, D. Closed-loop Control of Vortex Shedding in a Separated Diffuser Using an Inverse Method 2004 42nd AIAA Aerospace Sciences Meeting and Exhibit  DOI URL 
BibTeX:
@inproceedings{SuzukiColoniusMacMartin2004,
  author = {Suzuki, Takao and Colonius, Tim and MacMartin, Douglas},
  title = {Closed-loop Control of Vortex Shedding in a Separated Diffuser Using an Inverse Method},
  booktitle = {42nd AIAA Aerospace Sciences Meeting and Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2004},
  url = {http://colonius.caltech.edu/pdfs/SuzukiColoniusMacMartin2004.pdf},
  doi = {https://doi.org/10.2514/6.2004-577}
}
Suzuki, T., Colonius, T. and Pirozzoli, S. Vortex shedding in a two-dimensional diffuser: theory and simulation of separation control by periodic mass injection 2004 Journal of Fluid Mechanics
Vol. 520, pp. 187-213 
DOI URL 
Abstract: We develop a reduced-order model for large-scale unsteadiness (vortex shedding) in a two-dimensional diffuser and use the model to show how periodic mass injection near the separation point reduces stagnation pressure loss. The model estimates the characteristic frequency of vortex shedding and stagnation pressure loss by accounting for the accumulated circulation due to the vorticity flux into the separated region. The stagnation pressure loss consists of two parts: a steady part associated with the time-averaged static pressure distribution on the wall, and an unsteady part caused by vortex shedding. To validate the model, we perform numerical simulations of compressible unsteady laminar diffuser flows in two dimensions. The model and simulation show good agreement as we vary the Mach number and the area ratio of the diffuser. To investigate the effects of periodic mass injection near the separation point, we also perform simulations over a range of the injection frequencies. Periodic mass injection causes vortices to be pinched off with a smaller size as observed in experiments. Consequently, their convective velocity is increased, absorption of circulation from the wall is enhanced, and the reattached point is shifted upstream. Thus, in accordance with the model, the stagnation pressure loss, particularly the unsteady part, is substantially reduced even though the separation point is nearly unchanged. This study helps explain experimental results of separation control using unsteady mass injection in diffusers and on airfoils.
BibTeX:
@article{SuzukiColoniusPirozzoli2004,
  author = {Suzuki, T. and Colonius, T. and Pirozzoli, S.},
  title = {Vortex shedding in a two-dimensional diffuser: theory and simulation of separation control by periodic mass injection},
  journal = {Journal of Fluid Mechanics},
  year = {2004},
  volume = {520},
  pages = {187-213},
  url = {http://colonius.caltech.edu/pdfs/SuzukiColoniusPirozzoli2004.pdf},
  doi = {https://doi.org/10.1017/S0022112004001405}
}
Tanguay, M. Computation of bubbly cavitating flow in shock wave lithotripsy 2004 School: California Institute of Technology  URL 
Abstract: Lithotripsy is at the forefront of treatment of kidney stones. By firing shock waves at the stone, it can be broken down into small fragments. Although the treatment is non-invasive, both short- and long-term side effects occur. In order to understand and rectify these shortcomings, lithotripsy has been the subject of ongoing research. Based on in vitro experiments, it has been ascertained that the cloud of cavitating bubble produced in the wake of the shock wave is a crucial element in the stone comminution process.

Various solutions designed to maximize stone comminution and/or decrease tissue damage have been proposed over the years. However, the particulars of the comminution mechanism(s) are still undetermined. In this work, a numerical model of the two-phase flow inside an electrohydraulic lithotripter was used to provide additional insight in the behavior of the bubble cloud. The numerical model is based on an ensemble averaged two-phase flow model for a compressible liquid. The differential equations were discretized following the WENO shock capturing scheme in prolate spheroidal and cylindrical coordinate systems. The initial conditions for the flow field are estimated based on empirical observations and then validated by comparing the predicted pressure measurements and bubble cloud behavior against experimental values.

In order to gain additional insight in the mechanism for stone comminution, a variety of relevant initial conditions were modeled. The following lithotripter configurations were analyzed: free-field, dual-pulse and single-pulse with an artificial stone at the focus. The impact of parameters such as the intensity of the initial shock wave and the pulse rate frequency (PRF) has been investigated. Based on an energy argument, conclusions regarding the effciency of stone comminution are presented. In addition, based on these conclusions, avenues for improvement of the numerical model are highlighted.

BibTeX:
@phdthesis{Tanguay2004,
  author = {Tanguay, Michel},
  title = {Computation of bubbly cavitating flow in shock wave lithotripsy},
  school = {California Institute of Technology},
  year = {2004},
  url = {http://resolver.caltech.edu/CaltechETD:etd-05282004-130028}
}
Theofilis, V. and Colonius, T. Three-Dimensional Instabilities of Compressible Flow over Open Cavities: Direct Solution of hte BiGlobal Eivenvalue Problem 2004 34th AIAA Fluid Dynamics Conference and Exhibit  DOI URL 
BibTeX:
@inproceedings{TheofilisColonius2004,
  author = {Theofilis, Vassilis and Colonius, Tim},
  title = {Three-Dimensional Instabilities of Compressible Flow over Open Cavities: Direct Solution of hte BiGlobal Eivenvalue Problem},
  booktitle = {34th AIAA Fluid Dynamics Conference and Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2004},
  url = {http://colonius.caltech.edu/pdfs/TheofilisColonius2004.pdf},
  doi = {https://doi.org/10.2514/6.2004-2544}
}
Weinberg, K., Colonius, T. and Ortiz, M. A Model for Kidney Tissue Damage under High Speed Loading 2004 Proc. Appl. Math. Mech.
Vol. 4(1), pp. 234-235 
DOI URL 
Abstract: In a medical procedure to comminute kidney stones the patient is subjected to hypersonic waves focused at the stone. Unfortunately such shock waves also damage the surrounding kidney tissue. We present here a model for the mechanical response of the soft tissue to such a high speed loading regime. The material model combines shear induced plasticity with irreversible volumetric expansion as induced, e.g., by cavitating bubbles. The theory is based on a multiplicative decomposition of the deformation gradient and on an internal variable formulation of continuum thermodynamics. By the use of logarithmic and exponential mappings the stress update algorithms are extended from small-strain to the finite deformation range. In that way the time-discretized version of the porous-viscoplastic constitutive updates is described in a fully variational manner. By numerical experiments we study the shock-wave propagation into the tissue and analyze the resulting stress states. A first finite element simulation shows localized damage in the human kidney.
BibTeX:
@article{WeinbergColoniusOrtiz2004,
  author = {Kerstin Weinberg and Tim Colonius and Michael Ortiz},
  title = {A Model for Kidney Tissue Damage under High Speed Loading},
  journal = {Proc. Appl. Math. Mech.},
  year = {2004},
  volume = {4},
  number = {1},
  pages = {234--235},
  url = {http://colonius.caltech.edu/pdfs/WeinbergColoniusOrtiz2004.pdf},
  doi = {https://doi.org/10.1002/pamm.200410098}
}
Bailey, M.R., Cleveland, R.O., Colonius, T., Crum, L.A., Evan, A.P., Lingeman, J.E., McAteer, J.A., Sapozhnikov, O.A. and Williams, J.C. Cavitation in shock wave lithotripsy: The critical role of bubble activity in stone breakage and kidney trauma 2003 2003 IEEE Ultrasonics Symposium Proceedings, Vols 1 and 2, pp. 724-727  DOI URL 
Abstract: OBJECTIVE: Shock Wave Lithotripsy (SWL) is the use of shock waves to fragment kidney stones. We have undertaken a study of the physical mechanisms responsible for stone comminution and tissue injury in SWL. SWL was originally developed on the premise that stone fragmentation could be induced by a short duration, high amplitude positive pressure pulse. Even though the SWL waveform carries a prominent tensile component, it has long been thought that SW damage to stones could be explained entirely on the basis of mechanisms such as spallation, pressure gradients, and compressive fracture. We contend that not only is cavitation also involved in SWL, bubble activity plays a critical role in stone breakage and is a key mechanism in tissue damage. METHODS: Our evidence is based upon a series of experiments in which we have suppressed or minimized cavitation, and discovered that both stone comminution and tissue injury is similarly suppressed or minimized. Some examples of these experiments are (1) application of overpressure, (2) time reversal of acoustic waveform, (3) acoustically-transparent, cavitation-absorbing films, and (4) dual pulses. In addition, using passive and active ultrasound, we have observed the existence of cavitation, in vivo, and at the site of tissue injury. RESULTS: Numerical and experimental results showed mitigation of bubble collapse intensity by time-reversing the lithotripsy pulse and in vivo treatment showed a corresponding drop from 6.1% +/- 1.7% to 0.0% in the hemorrhagic lesion. The time-reversed wave did not break stones. Stone comminution and hemolysis were reduced to levels very near sham levels with the application of hydrostatic pressure greater than the near 10-MPa amplitude of the negative pressure of the lithotripter shock wave. A Mylar sheet 3-mm from the stone surface did not inhibit erosion and internal cracking, but a sheet in contact with the stone did. In water, mass lost from stones in a dual pulse lithotripter is 8 times greater than with a single lithotripter, but in glycerol, which reduces the pressures generated in bubble implosion, the enhancement is lost. CONCLUSION: This cavitation-inclusive mechanistic understanding of SWL is gaining acceptance and has had clinical impact. Treatment at slower SW rate gives cavitation bubble clusters time to dissolve between pulses and increases comminution. Some SWL centers now treat patients at slower SW rate to take advantage of this effect. An elegant cavitation-aware strategy to reduce renal trauma in SWL is being tested in experimental animals. Starting treatment at low amplitude causes vessels to constrict and this interferes with cavitation-mediated vascular injury. Acceptance of the role of cavitation in SWL is beginning to be embraced by the lithotripter industry, as new dual-pulse lithotripters-based on the concept of cavitation control- have now been introduced.
BibTeX:
@inproceedings{BaileyClevelandColoniusEtAl2003,
  author = {Bailey, M. R. and Cleveland, R. O. and Colonius, T. and Crum, L. A. and Evan, A. P. and Lingeman, J. E. and McAteer, J. A. and Sapozhnikov, O. A. and Williams, J. C.},
  title = {Cavitation in shock wave lithotripsy: The critical role of bubble activity in stone breakage and kidney trauma},
  booktitle = {2003 IEEE Ultrasonics Symposium Proceedings, Vols 1 and 2},
  year = {2003},
  pages = {724-727},
  url = {http://colonius.caltech.edu/pdfs/BaileyClevelandColoniusEtAl2003.pdf},
  doi = {https://doi.org/10.1109/ultsym.2003.1293503}
}
Bailey, M.R., Crum, L.A., Sapozhnikov, O.A., Evan, A.P., McAteer, J.A., Colonius, T. and Cleveland, R.O. Cavitation in shock wave lithotripsy 2003 146th Meeting of the Acoustical Society of America  DOI  
BibTeX:
@inproceedings{BaileyCrumSapozhnikovEtAl2003,
  author = {Bailey, Michael R. and Crum, Lawrence A. and Sapozhnikov, Oleg A. and Evan, Andrew P. and McAteer, James A. and Colonius, Tim and Cleveland, Robin O.},
  title = {Cavitation in shock wave lithotripsy},
  booktitle = {146th Meeting of the Acoustical Society of America},
  year = {2003},
  doi = {https://doi.org/10.1121/1.4778635}
}
Bertolotti, F. and Colonius, T. On the Noise Generated by Shear-Layer Instabilities in Turbulent Jets 2003 41st Aerospace Sciences Meeting and Exhibit  DOI URL 
BibTeX:
@inproceedings{BertolottiColonius2003,
  author = {Bertolotti, Fabio and Colonius, Tim},
  title = {On the Noise Generated by Shear-Layer Instabilities in Turbulent Jets},
  booktitle = {41st Aerospace Sciences Meeting and Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2003},
  url = {http://colonius.caltech.edu/pdfs/BertolottiColonius2003.pdf},
  doi = {https://doi.org/10.2514/6.2003-1062}
}
Colonius, T. and Tanguay, M. Cloud cavitation effects in shockwave lithotripsy 2003 146th Meeting of the Acoustical Society of America  DOI  
BibTeX:
@inproceedings{ColoniusTanguay2003,
  author = {Colonius, Tim and Tanguay, Michel},
  title = {Cloud cavitation effects in shockwave lithotripsy},
  booktitle = {146th Meeting of the Acoustical Society of America},
  year = {2003},
  doi = {https://doi.org/10.1121/1.4779511}
}
Pishchalnikov, Y.A., McAteer, J.A., Evan, A.P., Sapozhnikov, O.A., Cleveland, R.O., Colonius, T., Bailey, M.R. and Crum, L.A. Dynamics of concerted bubble cluster collapse in shock wave lithotripsy 2003 146th Meeting of the Acoustical Society of America  DOI  
BibTeX:
@inproceedings{PishchalnikovMcAteerEvanEtAl2003,
  author = {Pishchalnikov, Yuri A. and McAteer, James A. and Evan, Andrew P. and Sapozhnikov, Oleg A. and Cleveland, Robin O. and Colonius, Tim and Bailey, Michael R. and Crum, Lawrence A.},
  title = {Dynamics of concerted bubble cluster collapse in shock wave lithotripsy},
  booktitle = {146th Meeting of the Acoustical Society of America},
  year = {2003},
  doi = {https://doi.org/10.1121/1.4777748}
}
Pishchalnikov, Y.A., Sapozhnikov, O.A., Bailey, M.R., Williams, J.C., Cleveland, R.O., Colonius, T., Crum, L.A., Evan, A.P. and McAteer, J.A. Cavitation bubble cluster activity in the breakage of kidney stones by lithotripter shockwaves 2003 Journal of Endourology
Vol. 17(7), pp. 435-446 
DOI URL 
Abstract: Background and Purpose: There is strong evidence that cavitation bubble activity contributes to stone breakage and that shockwave-bubble interactions are involved in the tissue trauma associated with shockwave lithotripsy. Cavitation control may thus be a way to improve lithotripsy. Materials and Methods: High-speed photography was used to analyze cavitation bubble activity at the surface of artificial and natural kidney stones during exposure to lithotripter shockwaves in vitro.
Results: Numerous individual bubbles formed on the surfaces of stones, but these bubbles did not remain independent but rather combined to form clusters. Bubble clusters formed at the proximal and distal ends and at the sides of stones. Each cluster collapsed to a narrow point of impact. Collapse of the proximal cluster eroded the leading face of the stone, and the collapse of clusters at the sides of stones appeared to contribute to the growth of cracks. Collapse of the distal cluster caused minimal damage.
Conclusion: Cavitation-mediated damage to stones is attributable, not to the action of solitary bubbles, but to the growth and collapse of bubble clusters.
BibTeX:
@article{PishchalnikovSapozhnikovBaileyEtAl2003,
  author = {Pishchalnikov, Y. A. and Sapozhnikov, O. A. and Bailey, M. R. and Williams, J. C. and Cleveland, R. O. and Colonius, T. and Crum, L. A. and Evan, A. P. and McAteer, J. A.},
  title = {Cavitation bubble cluster activity in the breakage of kidney stones by lithotripter shockwaves},
  journal = {Journal of Endourology},
  year = {2003},
  volume = {17},
  number = {7},
  pages = {435-446},
  url = {http://colonius.caltech.edu/pdfs/PishchalnikovSapozhnikovBaileyEtAl2003.pdf},
  doi = {https://doi.org/10.1089/089277903769013568}
}
Preston, A., Colonius, T. and Brennen, C. Reduced-order modeling of diffusive effects on the dynamics of bubbles 2003 CAV2003: Fifth International Symposium on Cavitation, Osaka, Japan  URL 
BibTeX:
@inproceedings{PrestonColoniusBrennen2003,
  author = {Preston, A.T. and Colonius, T. and Brennen, C.E.},
  title = {Reduced-order modeling of diffusive effects on the dynamics of bubbles},
  booktitle = {CAV2003: Fifth International Symposium on Cavitation, Osaka, Japan},
  year = {2003},
  url = {http://colonius.caltech.edu/pdfs/PrestonColoniusBrennen2003.pdf}
}
Reba, R., Narayanan, S., Colonius, T. and Dunlop, M. A Study of the Role of Organized Structures in Jet Noise Generation 2003 9th AIAA/CEAS Aeroacoustics Conference and Exhibit  DOI URL 
BibTeX:
@inproceedings{RebaNarayananColoniusEtAl2003,
  author = {Reba, Ramons and Narayanan, Satish and Colonius, Tim and Dunlop, Mary},
  title = {A Study of the Role of Organized Structures in Jet Noise Generation},
  booktitle = {9th AIAA/CEAS Aeroacoustics Conference and Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2003},
  url = {http://colonius.caltech.edu/pdfs/RebaNarayananColoniusEtAl2003.pdf},
  doi = {https://doi.org/10.2514/6.2003-3314}
}
Suzuki, T. and Colonius, T. Inverse-imaging method for detection of a vortex in a channel 2003 AIAA Journal
Vol. 41(9), pp. 1743-1751 
DOI URL 
Abstract: A simple vortex-imaging algorithm using a least-square method is considered. The position and the circulation of a vortex convected in a channel are identified from the time history of pressure at a limited number of points on the wall. The capabilities of the algorithm are demonstrated using two-dimensional direct numerical simulations. A few observer points on one side of the wall are sufficient to detect the position and the circulation of a compact vortex to a reasonable degree of accuracy. An advanced algorithm can even detect two nearby vortices to the same degree of accuracy. Because the algorithm assumes a point vortex solution, the accuracy of the detection deteriorates as the vorticity distribution spreads.
BibTeX:
@article{SuzukiColonius2003,
  author = {Suzuki, T. and Colonius, T.},
  title = {Inverse-imaging method for detection of a vortex in a channel},
  journal = {AIAA Journal},
  year = {2003},
  volume = {41},
  number = {9},
  pages = {1743-1751},
  url = {http://colonius.caltech.edu/pdfs/SuzukiColonius2003.pdf},
  doi = {https://doi.org/10.2514/2.7292}
}
Suzuki, T. and Colonius, T. Large-scale Unsteadiness in a Two-dimensional Diffuser: Numerical Study Toward Active Separation Control 2003 41st Aerospace Sciences Meeting and Exhibit  DOI URL 
BibTeX:
@inproceedings{SuzukiColonius2003a,
  author = {Suzuki, Takao and Colonius, Tim},
  title = {Large-scale Unsteadiness in a Two-dimensional Diffuser: Numerical Study Toward Active Separation Control},
  booktitle = {41st Aerospace Sciences Meeting and Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2003},
  url = {http://colonius.caltech.edu/pdfs/SuzukiColonius2003a.pdf},
  doi = {https://doi.org/10.2514/6.2003-1138}
}
Suzuki, T., Colonius, T. and MacMartin, D. Inverse Technique for Vortex Imaging and Its Application to Feedback Flow Control 2003 33rd AIAA Fluid Dynamics Conference and Exhibit  DOI URL 
BibTeX:
@inproceedings{SuzukiColoniusMacMartin2003,
  author = {Suzuki, Takao and Colonius, Tim and MacMartin, Douglas},
  title = {Inverse Technique for Vortex Imaging and Its Application to Feedback Flow Control},
  booktitle = {33rd AIAA Fluid Dynamics Conference and Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2003},
  url = {http://colonius.caltech.edu/pdfs/SuzukiColoniusMacMartin2003.pdf},
  doi = {https://doi.org/10.2514/6.2003-4260}
}
Tanguay, M. and Colonius, T. Progress in modeling and simulation of shock wave lithotripsy (SWL). 2003 CAV2003: Fifth International Symposium on Cavitation, Osaka, Japan  URL 
BibTeX:
@inproceedings{TanguayColonius2003,
  author = {Tanguay, M. and Colonius, T.},
  title = {Progress in modeling and simulation of shock wave lithotripsy (SWL).},
  booktitle = {CAV2003: Fifth International Symposium on Cavitation, Osaka, Japan},
  year = {2003},
  url = {http://colonius.caltech.edu/pdfs/TanguayColonius2003.pdf}
}
Theofilis, V. and Colonius, T. An Algorithm for the Recovery of 2- and 3D BiGlobal Instabilities of Compressible Flow Over 2D Open Cavities 2003 33rd AIAA Fluid Dynamics Conference and Exhibit  DOI URL 
BibTeX:
@inproceedings{TheofilisColonius2003,
  author = {Theofilis, Vassilios and Colonius, Tim},
  title = {An Algorithm for the Recovery of 2- and 3D BiGlobal Instabilities of Compressible Flow Over 2D Open Cavities},
  booktitle = {33rd AIAA Fluid Dynamics Conference and Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2003},
  url = {http://colonius.caltech.edu/pdfs/TheofilisColonius2003.pdf},
  doi = {https://doi.org/10.2514/6.2003-4143}
}
Colonius, T. and Freund, J. POD analysis of sound generation by a turbulent jet 2002 40th AIAA Aerospace Sciences Meeting & Exhibit  DOI URL 
BibTeX:
@inproceedings{ColoniusFreund2002,
  author = {Colonius, T. and Freund, J.B.},
  title = {POD analysis of sound generation by a turbulent jet},
  booktitle = {40th AIAA Aerospace Sciences Meeting & Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2002},
  url = {http://colonius.caltech.edu/pdfs/ColoniusFreund2002.pdf},
  doi = {https://doi.org/10.2514/6.2002-72}
}
Colonius, T. and Freund, J. Reconstruction of large-scale structures and acoustic radiation from a turbulent M=0.9 jet using proper orthogonal decomposition 2002 Advances in Turbulence IX  URL 
BibTeX:
@inbook{ColoniusFreund2002a,
  author = {Colonius, T. and Freund, J.B.},
  title = {Reconstruction of large-scale structures and acoustic radiation from a turbulent M=0.9 jet using proper orthogonal decomposition},
  booktitle = {Advances in Turbulence IX},
  year = {2002},
  url = {http://colonius.caltech.edu/pdfs/ColoniusFreund2002a.pdf}
}
Colonius, T. and Ran, H.Y. A super-grid-scale model for simulating compressible flow on unbounded domains 2002 Journal of Computational Physics
Vol. 182(1), pp. 191-212 
DOI URL 
Abstract: A new buffer region (absorbing layer, sponge layer, fringe region) technique for computing compressible flows on unbounded domains is proposed. We exploit the connection between coordinate mapping from bounded to unbounded domains and filtering of the equations of motion in Fourier space in order to develop a model to damp flow disturbances (advective and acoustic) that propagate outside an arbitrarily defined near field. This effectively simulates a free-space boundary condition. Damping the solution in the far field is accomplished in a simple and effective way by applying a filter (similar to that used in large-eddy simulation) on a mesh in Fourier space, followed by a secondary filtering of the equations on the physical grid and implementation of a model for the unresolved scales. The final form of the buffer region is given in real space, independent of any discretization of the equations. Here we use a dealiased, Fourier spectral collocation method to demonstrate the efficacy of the buffer region for several model problems: acoustic wave propagation, convection of a finite-amplitude vortex, and a viscous starting jet in two dimensions. The results compare favorably to previous nonreflecting and absorbing boundary conditions.
BibTeX:
@article{ColoniusRan2002,
  author = {Colonius, T. and Ran, H. Y.},
  title = {A super-grid-scale model for simulating compressible flow on unbounded domains},
  journal = {Journal of Computational Physics},
  year = {2002},
  volume = {182},
  number = {1},
  pages = {191-212},
  url = {http://colonius.caltech.edu/pdfs/ColoniusRan2002.pdf},
  doi = {https://doi.org/10.1006/jcph.2002.7161}
}
Colonius, T., Rowley, C.W., Freund, J.B. and Murray, R.M. On the choice of norm for modeling compressible flow dynamics at reduced-order using the POD 2002 Proceedings of the 41st IEEE Conference on Decision and Control, Vols 1-4, pp. 3273-3278  DOI URL 
Abstract: We use POD/Galerkin projection to investigate and derive reduced-order models of the dynamics of compressible flows. We examine DNS data for two flows, a turbulent M=0.9 jet and self-sustained oscillations in the flow over an open cavity, and show how different choices of norm lead to different definitions of the energetic structures, and, for the cavity, to different reduced-order models of the dynamics. For the jet, we show that the near-field dynamics are fairly well represented by relatively few modes, but that key processes of interest, such a acoustic radiation, are not well captured by norms that are defined based on volume integrals of pressure and velocity. For the cavity flow, we demonstrate that vector-valued POD modes lead to reduced-order models that are much more effective (accurate and stable) than scalar-valued modes defined independently for different flow variables.
BibTeX:
@inproceedings{ColoniusRowleyFreundEtAl2002,
  author = {Colonius, T. and Rowley, C. W. and Freund, J. B. and Murray, R. M.},
  title = {On the choice of norm for modeling compressible flow dynamics at reduced-order using the POD},
  booktitle = {Proceedings of the 41st IEEE Conference on Decision and Control, Vols 1-4},
  year = {2002},
  pages = {3273--3278},
  url = {http://colonius.caltech.edu/pdfs/ColoniusRowleyFreundEtAl2002.pdf},
  doi = {https://doi.org/10.1109/cdc.2002.1184376}
}
Colonius, T. and Tanguay, M. Numerical simulation of shock and bubble dynamics in shockwave lithotripsy 2002 The First Pan-American/Iberian Meeting on Acoustics, Cancun, Mexico  DOI  
BibTeX:
@inproceedings{ColoniusTanguay2002,
  author = {Colonius, Tim and Tanguay, Michel},
  title = {Numerical simulation of shock and bubble dynamics in shockwave lithotripsy},
  booktitle = {The First Pan-American/Iberian Meeting on Acoustics, Cancun, Mexico},
  year = {2002},
  doi = {https://doi.org/10.1121/1.4779204}
}
Eldredge, J.D., Colonius, T. and Leonard, A. A dilating vortex particle method for compressible flow 2002 Journal of Turbulence
Vol. 3 
DOI URL 
Abstract: Vortex methods have become useful tools for the computation of incompressible fluid flow. In this work, a vortex particle method for the simulation of unsteady two-dimensional compressible flow is developed. By decomposing the velocity into irrotational and solenoidal parts, and using particles that are able to change volume and that carry vorticity, dilatation, enthalpy, entropy and density, the equations of motion are satisfied. Spatial derivatives are treated using the method of particle strength exchange with high-order-accurate, non-dissipative kernels. The new vortex method is applied to co-rotating and leapfrogging vortices in compressible flow, with the far acoustic field computed using a two-dimensional Kirchhoff surface.
BibTeX:
@article{EldredgeColoniusLeonard2002,
  author = {Eldredge, J. D. and Colonius, T. and Leonard, A.},
  title = {A dilating vortex particle method for compressible flow},
  journal = {Journal of Turbulence},
  year = {2002},
  volume = {3},
  url = {http://colonius.caltech.edu/pdfs/EldredgeColoniusLeonard2002.pdf},
  doi = {https://doi.org/10.1088/1468-5248/3/1/036}
}
Eldredge, J.D., Colonius, T. and Leonard, A. A vortex particle method for two-dimensional compressible flow 2002 Journal of Computational Physics
Vol. 179(2), pp. 371-399 
DOI URL 
Abstract: A vortex particle method is developed for simulating two-dimensional, unsteady compressible (low. The method uses the Helmholtz decomposition of the velocity field to separately treat the irrotational and solenoidal portions of the Now, and the particles are allowed to change volume to conserve mass. In addition to having vorticity and dilatation properties, the particles also carry density, enthalpy, and entropy. The resulting evolution equations contain terms that are computed with techniques used in some incompressible methods. Truncation of unbounded domains via a nonreflecting boundary condition is also considered. The fast multipole method is adapted to compressible particles in order to make the method computationally efficient. The new method is applied to several problems, including sound generation by corotating vortices and generation of vorticity by baroclinic torque.
BibTeX:
@article{EldredgeColoniusLeonard2002a,
  author = {Eldredge, J. D. and Colonius, T. and Leonard, A.},
  title = {A vortex particle method for two-dimensional compressible flow},
  journal = {Journal of Computational Physics},
  year = {2002},
  volume = {179},
  number = {2},
  pages = {371-399},
  url = {http://colonius.caltech.edu/pdfs/EldredgeColoniusLeonard2002a.pdf},
  doi = {https://doi.org/10.1006/jcph.2002.7060}
}
Eldredge, J.D., Leonard, A. and Colonius, T. A general deterministic treatment of derivatives in particle methods 2002 Journal of Computational Physics
Vol. 180(2), pp. 686-709 
DOI URL 
Abstract: A unified approach to approximating spatial derivatives in particle methods using integral operators is presented. The approach is an extension of particle strength exchange, originally developed for treating the Laplacian in advection-diffusion problems. Kernels of high order of accuracy are constructed that can be used to approximate derivatives of any degree. A new treatment for computing derivatives near the edge of particle coverage is introduced, using "one-sided" integrals that only look for information where it is available. The use of these integral approximations in wave propagation applications is considered and their error is analyzed in this context using Fourier methods. Finally, simple tests are performed to demonstrate the characteristics of the treatment, including an assessment of the effects of particle dispersion, and their results are discussed.
BibTeX:
@article{EldredgeLeonardColonius2002,
  author = {Eldredge, J. D. and Leonard, A. and Colonius, T.},
  title = {A general deterministic treatment of derivatives in particle methods},
  journal = {Journal of Computational Physics},
  year = {2002},
  volume = {180},
  number = {2},
  pages = {686-709},
  url = {http://colonius.caltech.edu/pdfs/EldredgeLeonardColonius2002.pdf},
  doi = {https://doi.org/10.1006/jcph.2002.7112}
}
Mohseni, K., Colonius, T. and Freund, J.B. An evaluation of linear instability waves as sources of sound in a supersonic turbulent jet 2002 Physics of Fluids
Vol. 14(10), pp. 3593-3600 
DOI URL 
Abstract: Mach wave radiation from supersonic jets is revisited to better quantify the extent to which linearized equations represent the details of the actual mechanism. To this end, we solve the linearized Navier-Stokes equations (LNS) with precisely the same mean flow and inflow disturbances as a previous direct numerical simulation (DNS) of a perfectly expanded turbulent M=1.92 jet [Freund , AIAA J. 38, 2023 (2000)]. We restrict our attention to the first two azimuthal modes, n=0 and n=1, which constitute most of the acoustic field. The direction of peak radiation and the peak Strouhal number matches the DNS reasonably well, which is in accord with previous experimental justification of the linear theory. However, it is found that the sound pressure level predicted by LNS is significantly lower than that from DNS. In order to investigate the discrepancy, individual frequency components of the solution are examined. These confirm that near the peak Strouhal number, particularly for the first helical mode n=1, the amplification of disturbances in the LNS closely matches the DNS. However, away from the peak frequency (and generally for the azimuthal mode n=0), modes in the LNS are damped while those in the DNS grow at rates comparable to those at the peak Strouhal number.
BibTeX:
@article{MohseniColoniusFreund2002,
  author = {Mohseni, K. and Colonius, T. and Freund, J. B.},
  title = {An evaluation of linear instability waves as sources of sound in a supersonic turbulent jet},
  journal = {Physics of Fluids},
  year = {2002},
  volume = {14},
  number = {10},
  pages = {3593-3600},
  url = {http://colonius.caltech.edu/pdfs/MohseniColoniusFreund2002.pdf},
  doi = {https://doi.org/10.1063/1.1501545}
}
Oh, K.-J. and Colonius, T. Large Eddy Simulation of the Compressible Flow Over an Open Cavity 2002 ASME 2002 Joint U.S.-European Fluids Engineering Division Conference  DOI  
BibTeX:
@inproceedings{OhColonius2002,
  author = {Keon-Je Oh and Tim Colonius},
  title = {Large Eddy Simulation of the Compressible Flow Over an Open Cavity},
  booktitle = {ASME 2002 Joint U.S.-European Fluids Engineering Division Conference},
  publisher = {ASME International},
  year = {2002},
  doi = {https://doi.org/10.1115/fedsm2002-31352}
}
Pishchalnikov, Y.A., Sapozhnikov, O.A., Bailey, M.R., Williams, J.C., Cleveland, R.O., Colonius, T., Crum, L.A., Evan, A.P. and McAteer, J.A. Cavitation damage to kidney stones in SWL involves the action of bubble clusters: New observations using ultra-high speed imaging in vitro 2002 Journal of Urology
Vol. 167(4), pp. 261-262 
URL 
BibTeX:
@article{PishchalnikovSapozhnikovBaileyEtAl2002,
  author = {Pishchalnikov, Y. A. and Sapozhnikov, O. A. and Bailey, M. R. and Williams, J. C. and Cleveland, R. O. and Colonius, T. and Crum, L. A. and Evan, A. P. and McAteer, J. A.},
  title = {Cavitation damage to kidney stones in SWL involves the action of bubble clusters: New observations using ultra-high speed imaging in vitro},
  journal = {Journal of Urology},
  year = {2002},
  volume = {167},
  number = {4},
  pages = {261-262},
  url = {http://colonius.caltech.edu/pdfs/PishchalnikovSapozhnikovBaileyEtAl2002.pdf}
}
Pishchalnikov, Y.A., Sapozhnikov, O.A., Williams, J.C., Evan, A.P., McAteer, J.A., Cleveland, R.O., Colonius, T., Bailey, M.R. and Crum, L.A. Cavitation bubble cluster activity in the breakage of stones by shock wave lithotripsy 2002 The First Pan-American/Iberian Meeting on Acoustics, Cancun, Mexico  DOI  
BibTeX:
@inproceedings{PishchalnikovSapozhnikovWilliamsEtAl2002,
  author = {Pishchalnikov, Yuriy A. and Sapozhnikov, Oleg A. and Williams, James C. and Evan, Andrew P. and McAteer, James A. and Cleveland, Robin O. and Colonius, Tim and Bailey, Michael R. and Crum, Lawrence A.},
  title = {Cavitation bubble cluster activity in the breakage of stones by shock wave lithotripsy},
  booktitle = {The First Pan-American/Iberian Meeting on Acoustics, Cancun, Mexico},
  year = {2002},
  doi = {https://doi.org/10.1121/1.4778494}
}
Preston, A., Colonius, T. and Brennen, C.E. A Reduced-Order Model of Heat Transfer Effects on the Dynamics of Bubbles 2002 ASME 2002 Joint U.S.-European Fluids Engineering Division Conference  DOI URL 
BibTeX:
@inproceedings{PrestonColoniusBrennen2002a,
  author = {Al Preston and Tim Colonius and Christopher E. Brennen},
  title = {A Reduced-Order Model of Heat Transfer Effects on the Dynamics of Bubbles},
  booktitle = {ASME 2002 Joint U.S.-European Fluids Engineering Division Conference},
  publisher = {ASME International},
  year = {2002},
  url = {http://colonius.caltech.edu/pdfs/PrestonColoniusBrennen2002a.pdf},
  doi = {https://doi.org/10.1115/FEDSM2002-31026}
}
Preston, A.T., Colonius, T. and Brennen, C.E. A numerical investigation of unsteady bubbly cavitating nozzle flows 2002 Physics of Fluids
Vol. 14(1), pp. 300-311 
DOI URL 
Abstract: The effects of unsteady bubble dynamics on cavitating flow through a converging-diverging nozzle are investigated numerically. A continuum model that couples the Rayleigh-Plesset equation with the continuity and momentum equations is used to formulate unsteady, quasi-one-dimensional partial differential equations. Flow regimes studied include those where steady-state solutions exist, and those where steady-state solutions diverge at the so-called flashing instability. These latter flows consist of unsteady bubbly shock waves traveling downstream in the diverging section of the nozzle. An approximate analytical expression is developed to predict the critical backpressure for choked flow. The results agree with previous barotropic models for those flows where bubble dynamics are not important, but show that in many instances the neglect of bubble dynamics cannot be justified. Finally the computations show reasonable agreement with an experiment that measures the spatial variation of pressure, velocity and void fraction for steady shockfree flows, and good agreement with an experiment that measures the throat pressure and shock position for flows with bubbly shocks. In the model, damping of the bubble radial motion is restricted to a simple "effective" viscosity, but many features of the flow are shown to be independent of the specific damping mechanism.
BibTeX:
@article{PrestonColoniusBrennen2002,
  author = {Preston, A. T. and Colonius, T. and Brennen, C. E.},
  title = {A numerical investigation of unsteady bubbly cavitating nozzle flows},
  journal = {Physics of Fluids},
  year = {2002},
  volume = {14},
  number = {1},
  pages = {300-311},
  url = {http://colonius.caltech.edu/pdfs/PrestonColoniusBrennen2002.pdf},
  doi = {https://doi.org/10.1063/1.1416497}
}
Rowley, C.W., Colonius, T. and Basu, A.J. On self-sustained oscillations in two-dimensional compressible flow over rectangular cavities 2002 Journal of Fluid Mechanics
Vol. 455, pp. 315-346 
DOI URL 
Abstract: Numerical simulations are used to investigate the resonant instabilities in two-dimensional flow past an open cavity. The compressible Navier-Stokes equations are solved directly (no turbulence model) for cavities with laminar boundary layers upstream. The computational domain is large enough to directly resolve a portion of the radiated acoustic field, which is shown to be in good visual agreement with schlieren photographs from experiments at several different Mach numbers. The results show a transition from a shear-layer mode, primarily for shorter cavities and lower Mach numbers, to a wake mode for longer cavities and higher Mach numbers. The shear-layer mode is characterized well by the acoustic feedback process described by Rossiter (1964), and disturbances in the shear layer compare well with predictions based on linear stability analysis of the Kelvin-Helmholtz mode. The wake mode is characterized instead by a large-scale vortex shedding with Strouhal number independent of Mach number. The wake mode oscillation is similar in many ways to that reported by Gharib & Roshko (1987) for incompressible flow with a laminar upstream boundary layer. Transition to wake mode occurs as the length and/or depth of the cavity becomes large compared to the upstream boundary-layer thickness, or as the Mach and/or Reynolds numbers are raised. Under these conditions, it is shown that the Kelvin-Helmholtz instability grows to sufficient strength that a strong recirculating flow is induced in the cavity. The resulting mean flow is similar to wake profiles that are absolutely unstable, and absolute instability may provide an explanation of the hydrodynamic feedback mechanism that leads to wake mode. Predictive criteria for the onset of shear-layer oscillations (from steady flow) and for the transition to wake mode are developed based on linear theory for amplification rates in the shear layer, and a simple model for the acoustic efficiency of edge scattering.
BibTeX:
@article{RowleyColoniusBasu2002,
  author = {Rowley, C. W. and Colonius, T. and Basu, A. J.},
  title = {On self-sustained oscillations in two-dimensional compressible flow over rectangular cavities},
  journal = {Journal of Fluid Mechanics},
  year = {2002},
  volume = {455},
  pages = {315-346},
  url = {http://colonius.caltech.edu/pdfs/RowleyColoniusBasu2002.pdf},
  doi = {https://doi.org/10.1017/S0022112001007534}
}
Rowley, C.W., Williams, D., Colonius, T., Murray, R., MacMartin, D. and Fabris, D. Model-based control of cavity oscillations. II - System identification and analysis 2002 40th AIAA Aerospace Sciences Meeting & Exhibit  DOI URL 
BibTeX:
@inproceedings{RowleyWilliamsColoniusEtAl2002,
  author = {Rowley, Clarence W. and Williams, David and Colonius, Tim and Murray, Richard and MacMartin, Douglas and Fabris, Drazin},
  title = {Model-based control of cavity oscillations. II - System identification and analysis},
  booktitle = {40th AIAA Aerospace Sciences Meeting & Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2002},
  url = {http://colonius.caltech.edu/pdfs/RowleyWilliamsColoniusEtAl2002.pdf},
  doi = {https://doi.org/10.2514/6.2002-972}
}
Tanguay, M. and Colonius, T. Numerical Investigation of Bubble Cloud Dynamics in Shock Wave Lithotripsy 2002 ASME 2002 Joint U.S.-European Fluids Engineering Division Conference  DOI URL 
BibTeX:
@inproceedings{TanguayColonius2002,
  author = {Michel Tanguay and Tim Colonius},
  title = {Numerical Investigation of Bubble Cloud Dynamics in Shock Wave Lithotripsy},
  booktitle = {ASME 2002 Joint U.S.-European Fluids Engineering Division Conference},
  publisher = {ASME International},
  year = {2002},
  url = {http://colonius.caltech.edu/pdfs/TanguayColonius2002.pdf},
  doi = {https://doi.org/10.1115/FEDSM2002-31010}
}
Theofilis, V., Sherwin, S. and Colonius, T. A unifying perspective of linear flow instabilities 2002 First Symposium on Global Flow Instability and Control, Crete, Greece   
BibTeX:
@inproceedings{TheofilisSherwinColonius2002,
  author = {Theofilis, V. and Sherwin, S.J. and Colonius, T.},
  title = {A unifying perspective of linear flow instabilities},
  booktitle = {First Symposium on Global Flow Instability and Control, Crete, Greece},
  year = {2002}
}
Williams, D., Rowley, C.W., Colonius, T., Murray, R., MacMartin, D., Fabris, D. and Albertson, J. Model-based control of cavity oscillations. I - Experiments 2002 40th AIAA Aerospace Sciences Meeting & Exhibit  DOI URL 
BibTeX:
@inproceedings{WilliamsRowleyColoniusEtAl2002,
  author = {Williams, David and Rowley, Clarence W. and Colonius, Tim and Murray, Richard and MacMartin, Douglas and Fabris, Drazin and Albertson, J.},
  title = {Model-based control of cavity oscillations. I - Experiments},
  booktitle = {40th AIAA Aerospace Sciences Meeting & Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2002},
  url = {http://colonius.caltech.edu/pdfs/WilliamsRowleyColoniusEtAl2002.pdf},
  doi = {https://doi.org/10.2514/6.2002-971}
}
Colonius, T. Advances in Aeroacoustics 2001 von Karman Institute for Fluid Dynamics Lecture Series 2001-02.   
BibTeX:
@inbook{Colonius2001,
  author = {Colonius, T.},
  title = {Advances in Aeroacoustics},
  booktitle = {von Karman Institute for Fluid Dynamics Lecture Series 2001-02.},
  publisher = {von Karman Institute for Fluid Dynamics},
  year = {2001}
}
Colonius, T. An overview of simulation, modeling, and active control of flow/acoustic resonance in open cavities 2001 39th Aerospace Sciences Meeting and Exhibit  DOI URL 
BibTeX:
@inproceedings{Colonius2001a,
  author = {Colonius, Tim},
  title = {An overview of simulation, modeling, and active control of flow/acoustic resonance in open cavities},
  booktitle = {39th Aerospace Sciences Meeting and Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2001},
  url = {http://colonius.caltech.edu/pdfs/Colonius2001a.pdf},
  doi = {https://doi.org/10.2514/6.2001-76}
}
Colonius, T. Computation of the sources of sound in turbulent flow 2001
Vol. 109141st Meeting of the Acoustical Society of America, pp. 1 
DOI  
Abstract: Direct numerical simulations of turbulent flows and their radiated acoustic fields offer a detailed description of the acoustic sources at low Reynolds number. High Reynolds number jets will remain inaccessible to direct computation for many years to come and there is thus a great need for good models of the acoustic sources. The low Reynolds number simulations can provide insight and data for such source modeling efforts. In this brief survey of research in this area issues that were anticipated in the research of Professor David Crighton for whom this session has been dedicated are discussed. These include the technical challenges that must be overcome in order to accurately compute aeroacoustic flows the modeling of acoustic sources in jets and mixing layers as wave packets and the scattering and refraction of sound by turbulence.
BibTeX:
@inproceedings{Colonius2001b,
  author = {Colonius, Tim},
  title = {Computation of the sources of sound in turbulent flow},
  booktitle = {141st Meeting of the Acoustical Society of America},
  year = {2001},
  volume = {109},
  pages = {1},
  doi = {https://doi.org/10.1121/1.4744852}
}
Colonius, T., Rowley, C. and Theofilis, V. Global instabilities and reduced-order models of cavity flow oscillations 2001 First Symposium on Global Flow Instability and Control   
BibTeX:
@inproceedings{ColoniusRowleyTheofilis2001,
  author = {Colonius, T. and Rowley, C.W. and Theofilis, V.},
  title = {Global instabilities and reduced-order models of cavity flow oscillations},
  booktitle = {First Symposium on Global Flow Instability and Control},
  year = {2001}
}
Eldredge, J. A dilating vortex particle method for compressible flow with application to aeroacoustics 2001 School: California Institute of Technology  URL 
Abstract: Vortex methods have become useful tools for the computation of incompressible fluid flow. In the present work, a vortex particle method for the simulation of unsteady two-dimensional compressible flow is developed and applied to several problems. The method is the first Langrangian simulation method for the full compressible Navier-Stokes equations. By decomposing the velocity into irrotational and solenoidal parts, and using particles that are able to change volume and that carry vorticity, dilation, enthalpy, entropy, and density, the equations of motion are satisfied. A general deterministic treatment of spatial derivatives in particle methods is developed by extending the method of particle strength exchange through the construction of higher-order-accurate, non-dissipative kernels for use in approximating arbitrary differential operators. The application of this technique to wave propagation problems is thoroughly explored. A one-sided operator is developed for approximating derivatives near the periphery of particle coverage; the operator is used to enforce a non-reflecting boundary condition for the absorption of acoustic waves at this periphery. Remeshing of the particles and the smooth interpolation of their strengths are addressed, and a criterion for the frequency of remeshing is developed on the principle axes of the rate-of-strain tensor. The fast multipole method for the fast summation of the velocity field is adapted for use with compressible particles. The new vortex method is applied to co-rotating and leapfrogging vortices in compressible flow, with the acoustic field computed using a two-dimensional Kirchoff surface, and the results agree will with those of previous work or analytical prediction. The method is also applied to the baroclinic generation of vorticity, and to the steepening of waves in the one-dimensional Burgers? equation, with favorable results in both case
BibTeX:
@phdthesis{Eldredge2001,
  author = {Eldredge, Jeff},
  title = {A dilating vortex particle method for compressible flow with application to aeroacoustics},
  school = {California Institute of Technology},
  year = {2001},
  url = {http://resolver.caltech.edu/CaltechETD:etd-12282004-113953}
}
Eldredge, J., Colonius, T. and Leonard, A. A vortex particle method for compressible flows 2001 15th AIAA Computational Fluid Dynamics Conference  DOI URL 
BibTeX:
@inproceedings{EldredgeColoniusLeonard2001,
  author = {Eldredge, Jeff and Colonius, Tim and Leonard, Anthony},
  title = {A vortex particle method for compressible flows},
  booktitle = {15th AIAA Computational Fluid Dynamics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2001},
  url = {http://colonius.caltech.edu/pdfs/EldredgeColoniusLeonard2001.pdf},
  doi = {https://doi.org/10.2514/6.2001-2641}
}
Mohseni, K., Colonius, T. and Freund, J. On the role of nonlinearity in Mach wave radiation in a Mach = 1.92 jet 2001 39th Aerospace Sciences Meeting and Exhibit  DOI URL 
BibTeX:
@inproceedings{MohseniColoniusFreund2001,
  author = {Mohseni, Kamran and Colonius, Tim and Freund, Jonathan},
  title = {On the role of nonlinearity in Mach wave radiation in a Mach = 1.92 jet},
  booktitle = {39th Aerospace Sciences Meeting and Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2001},
  url = {http://colonius.caltech.edu/pdfs/MohseniColoniusFreund2001.pdf},
  doi = {https://doi.org/10.2514/6.2001-377}
}
Mohseni, K., Ran, H.Y. and Colonius, T. Numerical experiments on vortex ring formation 2001 Journal of Fluid Mechanics
Vol. 430, pp. 267-282 
DOI URL 
Abstract: Numerical simulations are used to study the formation of vortex rings that are generated by applying a non-conservative force of long duration, simulating experimental vortex ring generation with large stroke ratio. For sufficiently long-duration forces, we investigate the extent to which properties of the leading vortex ring are invariant to the force distribution. The results confirm the existence of a universal 'formation number' defined by Gharib, Rambod & Shariff (1998), beyond which the leading vortex ring is separated from a trailing jet. We find that the formation process is governed by two non-dimensional parameters that are formed with three integrals of the motion (energy, circulation, and impulse) and the translation velocity of the leading vortex ring. Limiting values of the normalized energy and circulation of the leading vortex ring are found to be around 0.3 and 2.0, respectively, in agreement with the predictions of Mohseni & Gharib (1998). It is shown that under this normalization smaller variations in the circulation of the leading vortex ring are obtained than by scaling the circulation with parameters associated with the forcing. We show that by varying the spatial extent of the forcing or the forcing amplitude during the formation process, thicker rings with larger normalized circulation can be generated. Finally, the normalized energy and circulation of the leading vortex rings compare well with the same properties for vortices in the Norbury family with the same mean core radius.
BibTeX:
@article{MohseniRanColonius2001,
  author = {Mohseni, K. and Ran, H. Y. and Colonius, T.},
  title = {Numerical experiments on vortex ring formation},
  journal = {Journal of Fluid Mechanics},
  year = {2001},
  volume = {430},
  pages = {267-282},
  url = {http://colonius.caltech.edu/pdfs/MohseniRanColonius2001.pdf},
  doi = {https://doi.org/10.1017/s0022112000003025}
}
Preston, A., Colonius, T. and Brennen, C. Toward Efficient Computation of Heat and Mass Transfer Effects in the Continuum Model for Bubbly Cavitating Flows 2001 CAV 2001: Fourth International Symposium on Cavitation, Pasdena, CA  URL 
BibTeX:
@inproceedings{PrestonColoniusBrennen2001,
  author = {Preston, A.T. and Colonius, T. and Brennen, C.E.},
  title = {Toward Efficient Computation of Heat and Mass Transfer Effects in the Continuum Model for Bubbly Cavitating Flows},
  booktitle = {CAV 2001: Fourth International Symposium on Cavitation, Pasdena, CA},
  year = {2001},
  url = {http://colonius.caltech.edu/pdfs/PrestonColoniusBrennen2001.pdf}
}
Rowley, C. Modeling, simulation, and control of cavity flow oscillations 2001 School: California Institute of Technology  URL 
Abstract: This thesis involves the modeling of self-sustained oscillations in the flow past a rectangular cavity. The emphasis is on developing low-dimensional models that are suitable for analysis using tools from dynamical systems and control theory. Two-dimensional direct numerical simulations are performed, and indicate the presence of a ?wake mode,? which has been observed previously in experiments, but which is much less well understood than the ?shear-layer mode? usually observed. We characterize the flow in both shear-layer mode and wake mode, and provide a criterion for predicting the onset of wake mode, as a function of the various geometrical and flow-related parameters. We focus on the modeling of shear-layer mode, and employ two distinct modeling approaches: first, we use the method of Proper Orthogonal Decomposition (POD) and Galerkin projection to reduce the Navier-Stokes equations to a lowdimensional system of ordinary differential equations (ODEs). We extend the method to compressible flows, using approximations that are valid for cold flows at moderate Mach number. In a compressible flow, both the kinematic and thermodynamic variables contribute to the total energy, and an inner product is introduced which respects this, and allows one to use vector-valued POD modes for the Galerkin projection. We obtain models in the form of ODEs with between 2 and 60 states, and compare models based on scalar-valued and vector-valued POD modes. All of the models work well for short times (a few periods of oscillation), but the models based on scalar-valued modes deviate for longer times, while in general the models based on vector-valued modes retain qualitatively correct dynamical behavior. In the second modeling approach, we model the underlying physical mechanisms separately (shear-layer amplification, acoustic scattering, acoustic propagation), and obtain linear models that are suitable for control design and analysis. We design a controller which stabilizes the model, and implement a similar control law on an experiment, demonstrating significant reduction in the amplitude of the oscillations, but revealing some limitations of feedback control.
BibTeX:
@phdthesis{Rowley2001,
  author = {Rowley, Clarence},
  title = {Modeling, simulation, and control of cavity flow oscillations},
  school = {California Institute of Technology},
  year = {2001},
  url = {http://resolver.caltech.edu/CaltechETD:etd-12032004-075012}
}
Rowley, C., Colonius, T. and Murray, R. Dynamical models for control of cavity oscillations 2001 7th AIAA/CEAS Aeroacoustics Conference and Exhibit  DOI URL 
BibTeX:
@inproceedings{RowleyColoniusMurray2001,
  author = {Rowley, Clarence and Colonius, Tim and Murray, Richard},
  title = {Dynamical models for control of cavity oscillations},
  booktitle = {7th AIAA/CEAS Aeroacoustics Conference and Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2001},
  url = {http://colonius.caltech.edu/pdfs/RowleyColoniusMurray2001.pdf},
  doi = {https://doi.org/10.2514/6.2001-2126}
}
Tanguay, M. and Colonius, T. Numerical Simulation of Bubbly Cavitating Flow in Shock Wave Lithotripsy 2001 CAV 2001: Fourth International Symposium on Cavitation, Pasadena, CA  URL 
Abstract: The bubbly cavitating flow generated by a lithotriptor is computed using an ensemble averaged two-phase .ow model. The time-dependent, compressible .ow computation is divided into two separate calculations: the refocusing of a spherical pulse by an ellipsoidal re.ector, and the evolution of the steepening wave including the cavitating bubble cloud it generates. The .rst computation is single phase and is done in prolate spheroidal coordinates in order to have the surface of the ellipsoidal re.ector aligned with the computation grid. The output of this simulation is then fed to the two-phase cylindrical coordinates domain. Preliminary results and qualitative comparison to experimental observation are presented.
BibTeX:
@inproceedings{TanguayColonius2001,
  author = {Tanguay, M. and Colonius, T.},
  title = {Numerical Simulation of Bubbly Cavitating Flow in Shock Wave Lithotripsy},
  booktitle = {CAV 2001: Fourth International Symposium on Cavitation, Pasadena, CA},
  year = {2001},
  url = {http://colonius.caltech.edu/pdfs/TanguayColonius2001.pdf}
}
Colonius, T., d'Auria , F. and Brennen, C.E. Acoustic saturation in bubbly cavitating flow adjacent to an oscillating wall 2000 Physics of Fluids
Vol. 12(11), pp. 2752-2761 
DOI URL 
Abstract: Bubbly cavitating flow generated by the normal oscillation of a wall bounding a semi-infinite domain of fluid is computed using a continuum two-phase flow model. Bubble dynamics are computed, on the microscale, using the Rayleigh-Plesset equation. A Lagrangian finite volume scheme and implicit adaptive time marching are employed to accurately resolve bubbly shock waves and other steep gradients in the flow. The one-dimensional, unsteady computations show that when the wall oscillation frequency is much smaller than the bubble natural frequency, the power radiated away from the wall is limited by an acoustic saturation effect (the radiated power becomes independent of the amplitude of vibration), which is similar to that found in a pure gas. That is, for large enough vibration amplitude, nonlinear steepening of the generated waves leads to shocking of the wave train, and the dissipation associated with the jump conditions across each shock limits the radiated power. In the model, damping of the bubble volume oscillations is restricted to a simple "effective" viscosity. For wall oscillation frequency less than the bubble natural frequency, the saturation amplitude of the radiated field is nearly independent of any specific damping mechanism. Finally, implications for noise radiation from cavitating flows are discussed.
BibTeX:
@article{ColoniusBrennen2000,
  author = {Colonius, T. and d'Auria, F. and Brennen, C. E.},
  title = {Acoustic saturation in bubbly cavitating flow adjacent to an oscillating wall},
  journal = {Physics of Fluids},
  year = {2000},
  volume = {12},
  number = {11},
  pages = {2752-2761},
  url = {http://colonius.caltech.edu/pdfs/ColoniusBrennen2000.pdf},
  doi = {https://doi.org/10.1063/1.1313561}
}
Colonius, T. and Freund, J.B. Application of Lighthill's equation to Mach 1.92 turbulent jet 2000 AIAA Journal
Vol. 38(2), pp. 368-370 
DOI URL 
BibTeX:
@article{ColoniusFreund2000,
  author = {Colonius, T. and Freund, J. B.},
  title = {Application of Lighthill's equation to Mach 1.92 turbulent jet},
  journal = {AIAA Journal},
  year = {2000},
  volume = {38},
  number = {2},
  pages = {368-370},
  url = {http://colonius.caltech.edu/pdfs/ColoniusFreund2000.pdf},
  doi = {https://doi.org/10.2514/2.966}
}
Colonius, T., Rowley, C.W. and Murray, R.M. Simulation, modeling, and control of self-sustained oscillations in the flow past an open cavity 2000 XX ICTAM, Chicago IL   
BibTeX:
@inproceedings{ColoniusRowleyMurray2000,
  author = {Tim Colonius and Clarence W. Rowley and Richard M. Murray},
  title = {Simulation, modeling, and control of self-sustained oscillations in the flow past an open cavity},
  booktitle = {XX ICTAM, Chicago IL},
  year = {2000}
}
Eldredge, J., Colonius, T. and Leonard, A. Particle methods for compressible flows 2000 XX ICTAM, Chicago IL   
BibTeX:
@inproceedings{EldredgeColoniusLeonardLeonard2000,
  author = {Jeff Eldredge and Tim Colonius and Anthony Leonard},
  title = {Particle methods for compressible flows},
  booktitle = {XX ICTAM, Chicago IL},
  year = {2000}
}
Mohseni, K. A: Universality in vortex formation; B: Evaluation of Mach wave radiation in a supersonic jet. 2000 School: California Institute of Technology  URL 
Abstract: In this thesis two distinct features of coherent structures are investigated. In Part I a model for the pinch-off process in vortex ring formation is developed. The predicted nondimensional stroke length L/D (referred to as "formation number") satisfactorily matches experimental observations. The model introduces two nondimensional parameters that govern the limiting value of the formation number: a nondimensional energy and circulation, E_(nd) and \Gamma_(nd), respectively. The predicted value of E_(nd) also matches well with the experimental data. The limiting value for the new nondimensional circulation is predicted to be in the range 1.77 ≲ \Gamma_(nd) ≲ 2.07. We perform detailed computations of vortex ring formation by nonconservative forcing. The validity of the assumptions in our model is verified in these computations. Some techniques for generating fat rings are successfully investigated, resulting in generation of vortex rings with Hill's like properties. We consider thermodynamics of the vorticity density field (w/r), and we develop a statistical equilibrium theory for axisymmetric flows. It is shown that the statistical equilibrium of an axisymmetric flow is the state that maximizes an entropy functional constrained to the invariants of motion. Furthermore, it is shown that the final equilibrium state satisfies a variational principle similar to Kelvin's variational principle. In Part II Mach wave radiation mechanisms in a fully expanded supersonic jet is studied. We compare a direct numerical simulation (DNS) of a 1.92 Mach number jet with a linearized Navier-Stokes (LNS) simulation. The numerical integration technique, inflow boundary conditions, and grid distributions are the same in both simulations. We found that the generated noise in the DNS calculation is dominated by the first two azimuthal modes, and contributions from all other azimuthal modes were limited to less than 1.5 dB in the acoustic field. The total directivity of the sound field in the LNS matches reasonably well with the sound field of the DNS data. At the peak Strouhal frequency, particularly for the azimuthal mode n = 1, the amplification of flow variables in the LNS closely matches that of the DNS data. However, for frequencies away from the peak Strouhal number the DNS data shows amplification rates comparable to those of the peak Strouhal number, while in the LNS data any disturbances away from the peak Strouhal number are highly damped. These extra noise sources in the DNS data have the characteristics of a nonlinear interaction among various modes. The noise generated by the first two modes in the linearized computation is substantially weaker than in the DNS. For example, in the near acoustic field, at a distance of 6 jet diameters from the jet centerline, the sound pressure level in the linearized computation is as much as 8 db smaller than the DNS results. We observed that the maximum amplification rate for the DNS data occurs at an axial location further downstream than for the LNS data, which corresponds to regions around and beyond the end of the potential core. Our results indicate that the missing sound generation mechanisms in the LNS computation at the frequencies considered in this study can be attributed to the non-linear sound generation mechanisms, that are not captured in linear theories.
BibTeX:
@phdthesis{Mohseni2000,
  author = {Mohseni, Kamran},
  title = {A: Universality in vortex formation; B: Evaluation of Mach wave radiation in a supersonic jet.},
  school = {California Institute of Technology},
  year = {2000},
  url = {http://resolver.caltech.edu/CaltechTHESIS:10082010-114955709}
}
Mohseni, K. and Colonius, T. Numerical treatment of polar coordinate singularities 2000 Journal of Computational Physics
Vol. 157(2), pp. 787-795 
DOI URL 
BibTeX:
@article{MohseniColonius2000,
  author = {Mohseni, K. and Colonius, T.},
  title = {Numerical treatment of polar coordinate singularities},
  journal = {Journal of Computational Physics},
  year = {2000},
  volume = {157},
  number = {2},
  pages = {787-795},
  url = {http://colonius.caltech.edu/pdfs/MohseniColonius2000.pdf},
  doi = {https://doi.org/10.1006/jcph.1999.6382}
}
Preston, A., Colonius, T. and Brennen, C. A numerical investigation of unsteady bubbly caviating nozzle flows 2000 (FEDSM2000-11145)Fourth International Symposium on Numerical Methods for Multiphase Flow  URL 
BibTeX:
@inproceedings{PrestonColoniusBrennen2000,
  author = {Preston, A.T. and Colonius, T. and Brennen, C.E.},
  title = {A numerical investigation of unsteady bubbly caviating nozzle flows},
  booktitle = {Fourth International Symposium on Numerical Methods for Multiphase Flow},
  year = {2000},
  number = {FEDSM2000-11145},
  url = {http://colonius.caltech.edu/pdfs/PrestonColoniusBrennen2000.pdf}
}
Rowley, C., Colonius, T. and Murray, R. POD based models of self-sustained oscillations in the flow past an open cavity 2000 (AIAA-2000-1969)6th Aeroacoustics Conference and Exhibit  DOI URL 
BibTeX:
@inproceedings{RowleyColoniusMurray2000,
  author = {Rowley, Clarence and Colonius, Tim and Murray, Richard},
  title = {POD based models of self-sustained oscillations in the flow past an open cavity},
  booktitle = {6th Aeroacoustics Conference and Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {2000},
  number = {AIAA-2000-1969},
  url = {http://colonius.caltech.edu/pdfs/RowleyColoniusMurray2000.pdf},
  doi = {https://doi.org/10.2514/6.2000-1969}
}
Rowley, C.W. and Colonius, T. Discretely nonreflecting boundary conditions for linear hyperbolic systems 2000 Journal of Computational Physics
Vol. 157(2), pp. 500-538 
DOI URL 
Abstract: Many compressible flow and aeroacoustic computations rely on accurate nonreflecting or radiation boundary conditions. When the equations and boundary conditions are discretized using a finite-difference scheme, the dispersive nature of the discretized equations can lead to spurious numerical reflections not seen in the continuous boundary value problem. Here we construct discretely nonreflecting boundary conditions, which account for the particular finite-difference scheme used, and are designed to minimize these spurious numerical reflections. Stable boundary conditions that are local and nonreflecting to arbitrarily high order of accuracy are obtained, and test cases are presented for the linearized Euler equations. For the cases presented. reflections for a pressure pulse leaving the boundary are reduced by up to two orders of magnitude over typical ad hoc closures, and for a vorticity pulse, reflections are reduced by up to four orders of magnitude.
BibTeX:
@article{RowleyColonius2000,
  author = {Rowley, C. W. and Colonius, T.},
  title = {Discretely nonreflecting boundary conditions for linear hyperbolic systems},
  journal = {Journal of Computational Physics},
  year = {2000},
  volume = {157},
  number = {2},
  pages = {500-538},
  url = {http://colonius.caltech.edu/pdfs/RowleyColonius2000.pdf},
  doi = {https://doi.org/10.1006/jcph.1999.6383}
}
Zhou, J., Rusnak, F., Colonius, T. and Hathaway, G.M. Quasi-linear gradients for capillary liquid chromatography with mass and tandem mass spectrometry 2000 Rapid Communications in Mass Spectrometry
Vol. 14(6), pp. 432-438 
DOI URL 
Abstract: Gradient elution, capillary liquid chromatography mass spectrometry was performed with linear, static gradients constructed by laminar flowing ten, 1.5 mu L volume steps of decreasing organic concentration into tubing of small internal diameter. Sample loading, gradient formation, and sample elution were accomplished entirely by means of a commercially available micro-autosampler and single-syringe drive pump. The procedure was simple, fast, stable, and reproducible. Essentially linear gradients were produced without the use of additional valves, mixers, pumps or software. It took less than 10 minutes to form a gradient and less than 30 minutes to construct the set of individual buffer vials. The gradients were shown to be stable to storage. One hour after forming, peak retention times were reproduced to +/-0.5
%. Long-term retention time reproducibility was found to vary by +/-2%, Chromatographic resolution was comparable or superior to that obtained by gradient elution with conventional dynamic mixing and split how,
The procedure was adapted with a 'peak parking' method which extended the time for generating peptide fragmentation data up to 10 minutes per peptide with the triple quadruple mass spectrometer, Using this technique, collision data were collected at the 25 femtomole level on nine of ten tryptic peptides in a single run.
BibTeX:
@article{ZhouRusnakColoniusEtAl2000,
  author = {Zhou, J. and Rusnak, F. and Colonius, T. and Hathaway, G. M.},
  title = {Quasi-linear gradients for capillary liquid chromatography with mass and tandem mass spectrometry},
  journal = {Rapid Communications in Mass Spectrometry},
  year = {2000},
  volume = {14},
  number = {6},
  pages = {432-438},
  url = {http://colonius.caltech.edu/pdfs/ZhouRusnakColoniusEtAl2000.pdf},
  doi = {https://doi.org/10.1002/(sici)1097-0231(20000331)14:6%3C432::aid-rcm886%3E3.3.co;2-k}
}
Brennen, C., Colonius, T., Wang, Y.-C. and Preston, A. Cloud cavitation phenomena 1999 Twenty-Second Symposium on Naval Hydrodynamics  DOI URL 
BibTeX:
@inproceedings{BrennenColoniusWangEtAl1999,
  author = {Brennen, C.E and Colonius, T. and Wang, Y.-C. and Preston, A.T.},
  title = {Cloud cavitation phenomena},
  booktitle = {Twenty-Second Symposium on Naval Hydrodynamics},
  publisher = {The National Academies Press},
  year = {1999},
  url = {http://colonius.caltech.edu/pdfs/BrennenColoniusWangEtAl1999.pdf},
  doi = {https://doi.org/10.17226/9771}
}
Colonius, T. Direct numerical simulation of sound generation in turbulent shear flows 1999 137th Meeting of the Acoustical Society of America  DOI  
BibTeX:
@inproceedings{Colonius1999,
  author = {Colonius, Tim},
  title = {Direct numerical simulation of sound generation in turbulent shear flows},
  booktitle = {137th Meeting of the Acoustical Society of America},
  year = {1999},
  doi = {https://doi.org/10.1121/1.425824}
}
Colonius, T., Basu, A. and Rowley, C. Computation of sound generation and flow/acoustic instabilities in the flow past an open cavity 1999 Third ASME/JSME Joint Fluids Engineering Conference  URL 
BibTeX:
@inproceedings{ColoniusBasuRowley1999a,
  author = {Colonius, T. and Basu, A. and Rowley, C.W.},
  title = {Computation of sound generation and flow/acoustic instabilities in the flow past an open cavity},
  booktitle = {Third ASME/JSME Joint Fluids Engineering Conference},
  year = {1999},
  url = {http://colonius.caltech.edu/pdfs/ColoniusBasuRowley1999a.pdf}
}
Colonius, T., Basu, A. and Rowley, C. Numerical investigation of the flow past a cavity 1999 5th AIAA/CEAS Aeroacoustics Conference and Exhibit  DOI URL 
BibTeX:
@inproceedings{ColoniusBasuRowley1999,
  author = {Colonius, Tim and Basu, Amit and Rowley, Clarence},
  title = {Numerical investigation of the flow past a cavity},
  booktitle = {5th AIAA/CEAS Aeroacoustics Conference and Exhibit},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {1999},
  url = {http://colonius.caltech.edu/pdfs/ColoniusBasuRowley1999.pdf},
  doi = {https://doi.org/10.2514/6.1999-1912}
}
Kedia, R., Hunt, M.L. and Colonius, T. Transition of chaotic flow in a radially heated Taylor-Couette system 1999 Journal of Heat Transfer-Transactions of the Asme
Vol. 121(3), pp. 574-582 
DOI URL 
Abstract: Numerical simulations have been performed to study the stability of heated incompressible Taylor-Couette flow for a radius ratio of 0.7 and a Prandtl number of 0.7, As Gr is increased, the Taylor cell that has the same direction of circulation as the natural convection current increases in size and the counterrotating cell becomes smaller. The flow remains axisymmetric and the average heat transfer decreases with the increase in Gr. When the cylinder is impulsively heated, the counterrotating cell vanishes and n = 1 spiral is formed for Gr = 1000. This transition marks an increase in the hear transfer due to an increase in the radial velocity component of the fluid. By slowly varying the Grashof number, the simulations demonstrate the existence of a hysteresis loop. Two different stable states with same heat transfer are found to exist at the same Grashof number. A time-delay analysis of the radial velocity and the local heat transfer coefficient time is performed to determine the dimension at two Grashof numbers. For a fixed Reynolds number of 100, the two-dimensional projection of the reconstructed attractor shows a limit cycle for Gr = -1700. The limit cycle behavior disappears at Gr = -2100, and the reconstructed attractor becomes irregular. The attractor dimension increases to about 3.2 from a value of I for the limit cycle case, similar values were determined for both the local hear transfer and the local radial velocity, indicating that the dynamics of the temperature variations can be inferred from that of the velocity variations.
BibTeX:
@article{KediaHuntColonius1999,
  author = {Kedia, R. and Hunt, M. L. and Colonius, T.},
  title = {Transition of chaotic flow in a radially heated Taylor-Couette system},
  journal = {Journal of Heat Transfer-Transactions of the Asme},
  year = {1999},
  volume = {121},
  number = {3},
  pages = {574-582},
  url = {http://colonius.caltech.edu/pdfs/KediaHuntColonius1999.pdf},
  doi = {https://doi.org/10.1115/1.2826018}
}
Brennen, C., Colonius, T. and d'Auria , F. Computing shock waves in cloud cavitation 1998 Third International Symposium on Cavitation, Grenoble, France  URL 
BibTeX:
@inproceedings{BrennenColonius1998,
  author = {Brennen, C.E. and Colonius, T. and d'Auria, F.},
  title = {Computing shock waves in cloud cavitation},
  booktitle = {Third International Symposium on Cavitation, Grenoble, France},
  year = {1998},
  url = {http://colonius.caltech.edu/pdfs/BrennenColonius1998.pdf}
}
Colonius, T., Brennen, C. and d'Auria , F. Computation of shock waves in cavitating flows 1998 (FEDSM98-5027)Third International Symposium on Numerical Methods in Multiphase Flow  URL 
BibTeX:
@inproceedings{ColoniusBrennen1998,
  author = {Colonius, T. and Brennen, C.E. and d'Auria, F.},
  title = {Computation of shock waves in cavitating flows},
  booktitle = {Third International Symposium on Numerical Methods in Multiphase Flow},
  year = {1998},
  number = {FEDSM98-5027},
  url = {http://colonius.caltech.edu/pdfs/ColoniusBrennen1998.pdf}
}
Colonius, T., Mohseni, K., Freund, J., Lele, S. and Moin, P. Evaluation of Noise Radiation Mechanisms in Turbulent Jets 1998 Proceedings of the 1998 Summer Program  URL 
BibTeX:
@inproceedings{ColoniusMohseniFreundEtAl1998,
  author = {Colonius, T. and Mohseni, K. and Freund, J.B and Lele, S.K. and Moin, P.},
  title = {Evaluation of Noise Radiation Mechanisms in Turbulent Jets},
  booktitle = {Proceedings of the 1998 Summer Program},
  publisher = {Center for Turbulence Research},
  year = {1998},
  url = {http://colonius.caltech.edu/pdfs/ColoniusMohseniFreundEtAl1998.pdf}
}
Kedia, R., Hunt, M.L. and Colonius, T. Numerical simulations of heat transfer in Taylor-Couette flow 1998 Journal of Heat Transfer-Transactions of the Asme
Vol. 120(1), pp. 65-71 
DOI URL 
Abstract: Numerical simulations have been performed to study the effects of the gravitational and the centrifugal potentials on the stability of heated, incompressible Taylor-Couette flow. The flow is confined between two differentially heated, concentric cylinders, and the inner cylinder is allowed to rotate. The Navier-Stokes equations and the coupled energy equation are solved using a spectral method. To validate the code, comparisons are made with existing linear stability analysis and with experiments. The code is used to calculate the local and average heat transfer coefficients for a fixed Reynolds number (Re = 100) and a range of Grashof numbers. The investigation is primarily restricted to radius ratios 0.5 and 0.7 for fluids with Prandtl number of about 0.7. The variation of the local coefficients of heat transfer on the cylinder surface is investigated, and maps showing different stable states of the flow are presented. Results are also presented in terms of the equivalent conductivity, and show that heat transfer decreases with Grashof number in axisymmetric Taylor vortex flow regime, and increases with Grashof number after the flow becomes nonaxisymmetric.
BibTeX:
@article{KediaHuntColonius1998,
  author = {Kedia, R. and Hunt, M. L. and Colonius, T.},
  title = {Numerical simulations of heat transfer in Taylor-Couette flow},
  journal = {Journal of Heat Transfer-Transactions of the Asme},
  year = {1998},
  volume = {120},
  number = {1},
  pages = {65-71},
  url = {http://colonius.caltech.edu/pdfs/KediaHuntColonius1998.pdf},
  doi = {https://doi.org/10.1115/1.2830066}
}
Rowley, C. and Colonius, T. Numerically nonreflecting boundary conditions for multidimensional aeroacoustic computations 1998 4th AIAA/CEAS Aeroacoustics Conference  DOI URL 
BibTeX:
@inproceedings{RowleyColonius1998,
  author = {Rowley, Clarence and Colonius, Tim},
  title = {Numerically nonreflecting boundary conditions for multidimensional aeroacoustic computations},
  booktitle = {4th AIAA/CEAS Aeroacoustics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {1998},
  url = {http://colonius.caltech.edu/pdfs/RowleyColonius1998.pdf},
  doi = {https://doi.org/10.2514/6.1998-2220}
}
Colonius, T. Aeroacoustics and Active Noise Control 1997 von Karman Institute for Fluid Dynamics Lecture Series 1997-07  URL 
BibTeX:
@inbook{Colonius1997a,
  author = {Colonius, T.},
  title = {Aeroacoustics and Active Noise Control},
  booktitle = {von Karman Institute for Fluid Dynamics Lecture Series 1997-07},
  publisher = {von Karman Institute for Fluid Dynamics},
  year = {1997},
  url = {http://colonius.caltech.edu/pdfs/Colonius1997a.pdf}
}
Colonius, T. Numerically nonreflecting boundary and interface conditions for compressible flow and aeroacoustic computations 1997 AIAA Journal
Vol. 35(7), pp. 1126-1133 
DOI URL 
Abstract: Accurate nonreflecting or radiation boundary conditions are important for effective computation of aeroacoustic and compressible flow problems. The performance of such boundary conditions is often degraded upon discretization of the equations with finite difference and time marching methods. In particular, poorly resolved, spurious sawtooth waves are generated at boundaries due to the dispersive nature of the finite difference approximation. These disturbances can lead to spurious self-sustained oscillations in the flow (self-forcing), poor convergence to steady state, and long time instability of the numerics. Exact discretely nonreflecting boundary closures (boundary conditions for a downwind artificial boundary and an upwind physical boundary) are derived by considering a one-dimensional hyperbolic equation discretized with finite difference schemes and Runge-Kutta time advancements. The current methodology leads to stable local finite difference-like boundary closures, which are nonreflecting to an essentially arbitrarily high order of accuracy. These conditions can also be applied at interfaces where there is a discontinuity in the wave speed (a shock) or where there is an abrupt change in the grid spacing. Compared to other boundary treatments, the present boundary and interface conditions can reduce spurious reflected energy in the computational domain by many orders of magnitude.
BibTeX:
@article{Colonius1997,
  author = {Colonius, T.},
  title = {Numerically nonreflecting boundary and interface conditions for compressible flow and aeroacoustic computations},
  journal = {AIAA Journal},
  year = {1997},
  volume = {35},
  number = {7},
  pages = {1126-1133},
  url = {http://colonius.caltech.edu/pdfs/Colonius1997.pdf},
  doi = {https://doi.org/10.2514/2.235}
}
Colonius, T., Lele, S.K. and Moin, P. Sound generation in a mixing layer 1997 Journal of Fluid Mechanics
Vol. 330, pp. 375-409 
DOI URL 
Abstract: The sound generated by vortex pairing in a two-dimensional compressible mixing layer is investigated. Direct numerical simulations (DNS) of the Navier-Stokes equations are used to compute both the near-field region and a portion of the acoustic field. The acoustic analogy due to Lilley (1974) is also solved with acoustic sources determined from the near-field data of the DNS. It is shown that several commonly made simplifications to the acoustic sources can lead to erroneous predictions for the acoustic field, Predictions based on the quadrupole form of the source terms derived by Goldstein (1976a, 1984) are in excellent agreement with the acoustic field from the DNS. However, despite the low Mach number of the flow, the acoustic far field generated by the vortex pairings cannot be described by considering compact quadrupole sources. The acoustic sources have the form of modulated wave packets and the acoustic far field is described by a superdirective model (Crighton & Huerre 1990). The presence of flow-acoustic interactions in the computed source terms causes the acoustic field predicted by the acoustic analogy to be very sensitive to small changes in the description of the source.
BibTeX:
@article{ColoniusLeleMoin1997,
  author = {Colonius, T. and Lele, S. K. and Moin, P.},
  title = {Sound generation in a mixing layer},
  journal = {Journal of Fluid Mechanics},
  year = {1997},
  volume = {330},
  pages = {375-409},
  url = {http://colonius.caltech.edu/pdfs/ColoniusLeleMoin1997.pdf},
  doi = {https://doi.org/10.1017/s0022112096003928}
}
Colonius, T. Numerically nonreflecting boundary and interface conditions 1996 2nd AIAA/CEAS Aeroacoustics Conference  DOI  
BibTeX:
@inproceedings{Colonius1996,
  author = {Colonius, Tim},
  title = {Numerically nonreflecting boundary and interface conditions},
  booktitle = {2nd AIAA/CEAS Aeroacoustics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {1996},
  doi = {https://doi.org/10.2514/6.1996-1661}
}
Colonius, T. Aeroacoustics 1995 Aerospace America
Vol. 33(12), pp. 8-8 
 
BibTeX:
@article{Colonius1995,
  author = {Colonius, T.},
  title = {Aeroacoustics},
  journal = {Aerospace America},
  year = {1995},
  volume = {33},
  number = {12},
  pages = {8-8}
}
Colonius, T., Lele, S. and Moin, P. The sound generated by a two-dimensional shear layer: A comparison of direct computations and acoustic analogies 1995 1st AIAA/CEAS Aeroacoustics Conference  URL 
BibTeX:
@inproceedings{ColoniusLeleMoin1995,
  author = {Colonius, T. and Lele, S.K. and Moin, P.},
  title = {The sound generated by a two-dimensional shear layer: A comparison of direct computations and acoustic analogies},
  booktitle = {1st AIAA/CEAS Aeroacoustics Conference},
  year = {1995},
  url = {http://colonius.caltech.edu/pdfs/ColoniusLeleMoin1995.pdf}
}
Colonius, T., Lele, S. and Moin, P. The sound generated by a two-dimensional shear layer: The far field directivity from computations and acoustic analogies 1995
Vol. 219Computational Aeroacoustics 
URL 
BibTeX:
@inproceedings{ColoniusLeleMoin1995a,
  author = {Colonius, T. and Lele, S.K. and Moin, P.},
  title = {The sound generated by a two-dimensional shear layer: The far field directivity from computations and acoustic analogies},
  booktitle = {Computational Aeroacoustics},
  publisher = {ASME},
  year = {1995},
  volume = {219},
  url = {http://colonius.caltech.edu/pdfs/ColoniusLeleMoin1995a.pdf}
}
Colonius, T. Direct computation of aerodynamic sound generation 1994 School: Stanford University  URL 
BibTeX:
@phdthesis{Colonius1994,
  author = {Colonius, Tim},
  title = {Direct computation of aerodynamic sound generation},
  school = {Stanford University},
  year = {1994},
  url = {https://searchworks.stanford.edu/view/2949885}
}
Colonius, T., Lele, S.K. and Moin, P. The Scattering of Sound Waves by a Vortex -- Numerical Simulations and Analytical Solutions 1994 Journal of Fluid Mechanics
Vol. 260, pp. 271-298 
DOI URL 
Abstract: The scattering of plane sound waves by a vortex is investigated by solving the compressible Navier-Stokes equations numerically, and analytically with asymptotic expansions. Numerical errors associated with discretization and boundary conditions are made small by using high-order-accurate spatial differentiation and time marching schemes along with accurate non-reflecting boundary conditions. The accuracy of computations of flow fields with acoustic waves of amplitude five orders of magnitude smaller than the hydrodynamic fluctuations is directly verified. The properties of the scattered field are examined in detail. The results reveal inadequacies in previous vortex scattering theories when the circulation of the vortex is non-zero and refraction by the slowly decaying vortex flow field is important. Approximate analytical solutions that account for the refraction effect are developed and found to be in good agreement with the computations and experiments.
BibTeX:
@article{ColoniusLeleMoin1994,
  author = {Colonius, T. and Lele, S. K. and Moin, P.},
  title = {The Scattering of Sound Waves by a Vortex -- Numerical Simulations and Analytical Solutions},
  journal = {Journal of Fluid Mechanics},
  year = {1994},
  volume = {260},
  pages = {271-298},
  url = {http://colonius.caltech.edu/pdfs/ColoniusLeleMoin1994.pdf},
  doi = {https://doi.org/10.1017/s0022112094003514}
}
Colonius, T., Lele, S. and Moin, P. Direct computation of the sound generated by two-dimensional shear layer 1993 15th Aeroacoustics Conference  DOI URL 
BibTeX:
@inproceedings{ColoniusLeleMoin1993a,
  author = {Colonius, Tim and Lele, Sanjiva and Moin, Parviz},
  title = {Direct computation of the sound generated by two-dimensional shear layer},
  booktitle = {15th Aeroacoustics Conference},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {1993},
  url = {http://colonius.caltech.edu/pdfs/ColoniusLeleMoin1993a.pdf},
  doi = {https://doi.org/10.2514/6.1993-4328}
}
Colonius, T., Lele, S.K. and Moin, P. Boundary Conditions for Direct Computation of Aerodynamic Sound Generation 1993 AIAA Journal
Vol. 31(9), pp. 1574-1582 
DOI URL 
Abstract: Accurate computation of the far-field sound along with the near-field source terms associated with a free shear flow requires that the Navier-Stokes equations be solved using accurate numerical differentiation and time-marching schemes, with nonreflecting boundary conditions. Nonreflecting boundary conditions have been developed for two-dimensional linearized Euler equations by Giles. These conditions are modified for use with nonlinear Navier-Stokes computations of open flow problems. At an outflow, vortical structures are found to produce large reflections due to nonlinear effects; these reflection errors cannot be improved by increasing the accuracy of the linear boundary conditions. An exit zone just upstream of an outflow where disturbances are significantly attenuated through grid stretching and filtering is developed for use with the nonreflecting boundary conditions; reflections from vortical structures are decreased by 3 orders of magnitude. The accuracy and stability of the boundary conditions are investigated in several model flows that include sound radiation by an energy source in a uniformly sheared viscous flow, the propagation of vortices in a uniform flow, and the spatial evolution of a compressible mixing layer.
BibTeX:
@article{ColoniusLeleMoin1993,
  author = {Colonius, T. and Lele, S. K. and Moin, P.},
  title = {Boundary Conditions for Direct Computation of Aerodynamic Sound Generation},
  journal = {AIAA Journal},
  year = {1993},
  volume = {31},
  number = {9},
  pages = {1574-1582},
  url = {http://colonius.caltech.edu/pdfs/ColoniusLeleMoin1993.pdf},
  doi = {https://doi.org/10.2514/3.11817}
}
Colonius, T., Lele, S. and Moin, P. Boundary conditions for direct computation of aerodynamic sound generation 1992 (DGLR/AIAA-92-02-075)DGLR/AIAA 14th Aeroacoustics Conference   
BibTeX:
@inproceedings{ColoniusLeleMoin1992,
  author = {Colonius, T. and Lele, S.K. and Moin, P.},
  title = {Boundary conditions for direct computation of aerodynamic sound generation},
  booktitle = {DGLR/AIAA 14th Aeroacoustics Conference},
  year = {1992},
  number = {DGLR/AIAA-92-02-075}
}
Colonius, T., Lele, S. and Moin, P. Scattering of sound waves by a compressible vortex 1991 29th Aerospace Sciences Meeting  DOI URL 
BibTeX:
@inproceedings{ColoniusLeleMoin1991a,
  author = {Colonius, Tim and Lele, Sanjiva and Moin, Parviz},
  title = {Scattering of sound waves by a compressible vortex},
  booktitle = {29th Aerospace Sciences Meeting},
  publisher = {American Institute of Aeronautics and Astronautics},
  year = {1991},
  url = {http://colonius.caltech.edu/pdfs/ColoniusLeleMoin1991a.pdf},
  doi = {https://doi.org/10.2514/6.1991-494}
}
Colonius, T., Lele, S.K. and Moin, P. The Free Compressible Viscous Vortex 1991 Journal of Fluid Mechanics
Vol. 230, pp. 45-73 
DOI URL 
Abstract: The effects of compressibility on free (unsteady) viscous heat-conducting vortices are investigated. Analytical solutions are found in the limit of large, but finite, Reynolds number, and small, but finite, Mach number. The analysis shows that the spreading of the vortex causes a radial flow. This flow is given by the solution of an ordinary differential equation (valid for any Mach number), which gives the dependence of the radial velocity on the tangential velocity, density, and temperature profiles of the vortex; estimates of the radial velocity found by solving this equation are found to be in good agreement with numerical solutions of the full equations. The experiments of Mandella (1987) also report a radial flow in the vortex, but their estimates are much larger than the analytical predictions, and it is found that the flow inferred from the experiments violates the Second Law of Thermodynamics for two-dimensional axisymmetric flow. It is speculated that three-dimensionality is the cause of this discrepancy. To obtain detailed analytical solutions, the equations for the viscous evolution are expanded in powers of Mach number, M. Solutions valid to O(M2), are discussed for vortices with finite circulation. Two specific initial conditions - vortices with initially uniform entropy and with initially uniform density - are analysed in detail. It is shown that swirling axisymmetric compressible flows generate negative radial velocities far from the vortex core owing to viscous effects, regardless of the initial distributions of vorticity, density and entropy.
BibTeX:
@article{ColoniusLeleMoin1991,
  author = {Colonius, T. and Lele, S. K. and Moin, P.},
  title = {The Free Compressible Viscous Vortex},
  journal = {Journal of Fluid Mechanics},
  year = {1991},
  volume = {230},
  pages = {45-73},
  url = {http://colonius.caltech.edu/pdfs/ColoniusLeleMoin1991.pdf},
  doi = {https://doi.org/10.1017/s0022112091000708}
}