Article records
https://feeds.library.caltech.edu/people/Rowley-C-W/article.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 14:13:12 +0000Discretely Nonreflecting Boundary Conditions for Linear Hyperbolic Systems
https://resolver.caltech.edu/CaltechAUTHORS:20190726-104729508
Authors: {'items': [{'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Colonius-T', 'name': {'family': 'Colonius', 'given': 'Tim'}, 'orcid': '0000-0003-0326-3909'}]}
Year: 2000
DOI: 10.1006/jcph.1999.6383
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.https://authors.library.caltech.edu/records/ag9g2-5de13Reconstruction equations and the Karhunen–Loève expansion for systems with symmetry
https://resolver.caltech.edu/CaltechAUTHORS:20100913-105958467
Authors: {'items': [{'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'Jerrold E.'}}]}
Year: 2000
DOI: 10.1016/S0167-2789(00)00042-7
We present a method for applying the Karhunen–Loève decomposition to systems with continuous symmetry. The techniques in this paper contribute to the general procedure of removing variables associated with the symmetry of a problem, and related ideas have been used in previous works both to identify coherent structures in solutions of PDEs, and to derive low-order models via Galerkin projection. The main result of this paper is to derive a simple and easily implementable set of reconstruction equationswhich close the system of ODEs produced by Galerkin projection. The geometric interpretation of the method closely parallels techniques used in geometric phases and reconstruction techniques in geometric mechanics. We apply the method to the Kuramoto–Sivashinsky equation and are able to derive accurate models of considerably lower dimension than are possible with the traditional Karhunen–Loève expansion.https://authors.library.caltech.edu/records/mvwyn-fnf79Reconstruction Equations and the Karhunen-Loève
Expansion for Systems with Symmetry
https://resolver.caltech.edu/CaltechAUTHORS:20101025-090642137
Authors: {'items': [{'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'Jerrold E.'}}]}
Year: 2000
DOI: 10.1016/S0167-2789(00)00042-7
We present a method for applying the Karhunen-Lo`eve decomposition to
systems with continuous symmetry. The techniques in this paper contribute to
the general procedure of removing variables associated with the symmetry of a
problem, and related ideas have been used in previous works both to identify
coherent structures in solutions of PDEs, and to derive low-order models via
Galerkin projection. The main result of this paper is to derive a simple and
easily implementable set of reconstruction equations which close the system of
ODEs produced by Galerkin projection. The geometric interpretation of the
method closely parallels techniques used in geometric phases and reconstruction
techniques in geometric mechanics. We apply the method to the Kuramoto-
Sivashinsky equation and are able to derive accurate models of considerably
lower dimension than are possible with the traditional Karhunen-Loève expansion.https://authors.library.caltech.edu/records/vnr3y-9ah91On self-sustained oscillations in two-dimensional compressible flow over rectangular cavities
https://resolver.caltech.edu/CaltechAUTHORS:ROWjfm02
Authors: {'items': [{'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Colonius-T', 'name': {'family': 'Colonius', 'given': 'Tim'}, 'orcid': '0000-0003-0326-3909'}, {'id': 'Basu-A-J', 'name': {'family': 'Basu', 'given': 'Amit J.'}}]}
Year: 2002
DOI: 10.1017/S0022112001007534
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.https://authors.library.caltech.edu/records/jzmer-yr644Reduction and reconstruction for self-similar dynamical systems
https://resolver.caltech.edu/CaltechAUTHORS:ROWnonlin03
Authors: {'items': [{'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Kevrekidis-I-G', 'name': {'family': 'Kevrekidis', 'given': 'Ioannis G.'}}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'Jerrold E.'}}, {'id': 'Lust-K', 'name': {'family': 'Lust', 'given': 'Kurt'}}]}
Year: 2003
DOI: 10.1088/0951-7715/16/4/304
We present a general method for analysing and numerically solving partial differential equations with self-similar solutions. The method employs ideas from symmetry reduction in geometric mechanics, and involves separating the dynamics on the shape space (which determines the overall shape of the solution) from those on the group space (which determines the size and scale of the solution). The method is computationally tractable as well, allowing one to compute self-similar solutions by evolving a dynamical system to a steady state, in a scaled reference frame where the self-similarity has been factored out. More generally, bifurcation techniques can be used to find self-similar solutions, and determine their behaviour as parameters in the equations are varied.https://authors.library.caltech.edu/records/yxzv6-6sa77Model reduction for compressible flows using POD and Galerkin projection
https://resolver.caltech.edu/CaltechAUTHORS:20190214-075224908
Authors: {'items': [{'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Colonius-T', 'name': {'family': 'Colonius', 'given': 'Tim'}, 'orcid': '0000-0003-0326-3909'}, {'id': 'Murray-R-M', 'name': {'family': 'Murray', 'given': 'Richard M.'}, 'orcid': '0000-0002-5785-7481'}]}
Year: 2004
DOI: 10.1016/j.physd.2003.03.001
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.https://authors.library.caltech.edu/records/2fex1-0xr95Locomotion of Articulated Bodies in a Perfect Fluid
https://resolver.caltech.edu/CaltechAUTHORS:20100819-133718721
Authors: {'items': [{'id': 'Kanso-E', 'name': {'family': 'Kanso', 'given': 'E.'}}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'J. E.'}}, {'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'C. W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Melli-Huber-J-B', 'name': {'family': 'Melli-Huber', 'given': 'J. B.'}}]}
Year: 2005
DOI: 10.1007/s00332-004-0650-9
This paper is concerned with modeling the dynamics of N articulated solid bodies submerged in an ideal fluid. The model is used to analyze the locomotion of aquatic animals due to the coupling between their shape changes and the fluid dynamics in their environment. The equations of motion are obtained by making use of a two-stage reduction process which leads to significant mathematical and computational simplifications. The first reduction exploits particle relabeling symmetry: that is, the symmetry associated with the conservation of circulation for ideal, incompressible fluids. As a result, the equations of motion for the submerged solid bodies can be formulated without explicitly incorporating the fluid variables. This reduction by the fluid variables is a key difference with earlier methods, and it is appropriate since one is mainly interested in the location of the bodies, not the fluid particles. The second reduction is associated with the invariance of the dynamics under superimposed rigid motions. This invariance corresponds to the conservation of total momentum of the solid-fluid system. Due to this symmetry, the net locomotion of the solid system is realized as the sum of geometric and dynamic phases over the shape space consisting of allowable relative motions, or deformations, of the solids. In particular, reconstruction equations that govern the net locomotion at zero momentum, that is, the geometric phases, are obtained. As an illustrative example, a planar three-link mechanism is shown to propel and steer itself at zero momentum by periodically changing its shape. Two solutions are presented: one corresponds to a hydrodynamically decoupled mechanism and one is based on accurately computing the added inertias using a boundary element method. The hydrodynamically decoupled model produces smaller net motion than the more accurate model, indicating that it is important to consider the hydrodynamic interaction of the links.https://authors.library.caltech.edu/records/btmc2-w3m96Linear models for control of cavity flow oscillations
https://resolver.caltech.edu/CaltechAUTHORS:ROWjfm06
Authors: {'items': [{'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Williams-D-R', 'name': {'family': 'Williams', 'given': 'David R.'}}, {'id': 'Colonius-T', 'name': {'family': 'Colonius', 'given': 'Tim'}, 'orcid': '0000-0003-0326-3909'}, {'id': 'Murray-R-M', 'name': {'family': 'Murray', 'given': 'Richard M.'}, 'orcid': '0000-0002-5785-7481'}, {'id': 'MacMartin-D-G', 'name': {'family': 'MacMynowski', 'given': 'Douglas G.'}, 'orcid': '0000-0003-1987-9417'}]}
Year: 2006
DOI: 10.1017/S0022112005007299
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.https://authors.library.caltech.edu/records/cs1cy-78146Lift Enhancement for Low-Aspect-Ratio Wings with Periodic Excitation
https://resolver.caltech.edu/CaltechAUTHORS:20100831-130506686
Authors: {'items': [{'id': 'Taira-Kunihiko', 'name': {'family': 'Taira', 'given': 'Kunihiko'}, 'orcid': '0000-0002-3762-8075'}, {'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Colonius-T', 'name': {'family': 'Colonius', 'given': 'Tim'}, 'orcid': '0000-0003-0326-3909'}, {'id': 'Williams-D-R', 'name': {'family': 'Williams', 'given': 'David R.'}}]}
Year: 2010
DOI: 10.2514/1.J050248
In an effort to enhance lift on low-aspect-ratio rectangular flat-plate wings in low-Reynolds-number
post-stall 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.https://authors.library.caltech.edu/records/kjydr-yaz92Modal Analysis of Fluid Flows: An Overview
https://resolver.caltech.edu/CaltechAUTHORS:20171213-075938896
Authors: {'items': [{'id': 'Taira-Kunihiko', 'name': {'family': 'Taira', 'given': 'Kunihiko'}, 'orcid': '0000-0002-3762-8075'}, {'id': 'Brunton-S-L', 'name': {'family': 'Brunton', 'given': 'Steven L.'}}, {'id': 'Dawson-S-T-M', 'name': {'family': 'Dawson', 'given': 'Scott T. M.'}, 'orcid': '0000-0002-0020-2097'}, {'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Colonius-T', 'name': {'family': 'Colonius', 'given': 'Tim'}, 'orcid': '0000-0003-0326-3909'}, {'id': 'McKeon-B-J', 'name': {'family': 'McKeon', 'given': 'Beverley J.'}, 'orcid': '0000-0003-4220-1583'}, {'id': 'Schmidt-O-T', 'name': {'family': 'Schmidt', 'given': 'Oliver T.'}, 'orcid': '0000-0002-7097-0235'}, {'id': 'Gordeyev-S', 'name': {'family': 'Gordeyev', 'given': 'Stanislav'}}, {'id': 'Theofilis-V', 'name': {'family': 'Theofilis', 'given': 'Vassilios'}}, {'id': 'Ukeiley-L-S', 'name': {'family': 'Ukeiley', 'given': 'Lawrence S.'}}]}
Year: 2017
DOI: 10.2514/1.J056060
Simple aerodynamic configurations under even modest conditions can exhibit complex flows with a wide range of temporal and spatial features. It has become common practice in the analysis of these flows to look for and extract physically important features, or modes, as a first step in the analysis. This step typically starts with a modal decomposition of an experimental or numerical dataset of the flowfield, or of an operator relevant to the system. We describe herein some of the dominant techniques for accomplishing these modal decompositions and analyses that have seen a surge of activity in recent decades [1–8]. For a nonexpert, keeping track of recent developments can be daunting, and the intent of this document is to provide an introduction to modal analysis that is accessible to the larger fluid dynamics community. In particular, we present a brief overview of several of the well-established techniques and clearly lay the framework of these methods using familiar linear algebra. The modal analysis techniques covered in this paper include the proper orthogonal decomposition (POD), balanced proper orthogonal decomposition (balanced POD), dynamic mode decomposition (DMD), Koopman analysis, global linear stability analysis, and resolvent analysis.https://authors.library.caltech.edu/records/q7fn7-mdy41