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Low-Dimensional Modelling of Turbulence Using the Proper Orthogonal Decomposition: A Tutorial

Smith, Troy R. and Moehlis, Jeff and Holmes, Philip (2005) Low-Dimensional Modelling of Turbulence Using the Proper Orthogonal Decomposition: A Tutorial. Nonlinear Dynamics, 41 (1-3). pp. 275-307. ISSN 0924-090X. doi:10.1007/s11071-005-2823-y. https://resolver.caltech.edu/CaltechAUTHORS:20200324-150549343

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Abstract

The proper orthogonal decomposition identifies basis functions or modes which optimally capture the average energy content from numerical or experimental data. By projecting the Navier–Stokes equations onto these modes and truncating, one can obtain low-dimensional ordinary differential equation models for fluid flows. In this paper we present a tutorial on the construction of such models. In addition to providing a general overview of the procedure, we describe two different ways to numerically calculate the modes, show how symmetry considerations can be exploited to simplify and understand them, comment on how parameter variations are captured naturally in such models, and describe a generalization of the procedure involving projection onto uncoupled modes that allow streamwise and cross-stream components to evolve independently. We illustrate for the example of plane Couette flow in a minimal flow unit – a domain whose spanwise and streamwise extent is just sufficient to maintain turbulence.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s11071-005-2823-yDOIArticle
https://rdcu.be/b3dlwPublisherFree ReadCube access
Additional Information:© 2005 Springer. Received 06 January 2004; Accepted 22 January 2004. This work was supported by DoE: DE-FG02-95ER25238 (T.S. and P.H.) and a National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship to J.M. We thank Clancy Rowley for allowing the use, and modification, of his channel flow code.
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG02-95ER25238
NSF Postdoctoral FellowshipUNSPECIFIED
Subject Keywords:plane Couette flow; proper orthogonal decomposition; turbulence
Issue or Number:1-3
DOI:10.1007/s11071-005-2823-y
Record Number:CaltechAUTHORS:20200324-150549343
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200324-150549343
Official Citation:SMITH, T.R., MOEHLIS, J. & HOLMES, P. Low-Dimensional Modelling of Turbulence Using the Proper Orthogonal Decomposition: A Tutorial. Nonlinear Dyn 41, 275–307 (2005). https://doi.org/10.1007/s11071-005-2823-y
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:102090
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:24 Mar 2020 22:20
Last Modified:16 Nov 2021 18:08

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