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Computing exact coherent states in channels starting from the laminar profile: A resolvent-based approach

Rosenberg, Kevin and McKeon, Beverley J. (2019) Computing exact coherent states in channels starting from the laminar profile: A resolvent-based approach. Physical Review E, 100 (2). Art. No. 021101. ISSN 2470-0045. doi:10.1103/physreve.100.021101.

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We present an iterative method to compute traveling wave exact coherent states (ECS) in Couette and Poiseuille flows starting from an initial laminar profile. The approach utilizes the resolvent operator for a two-dimensional, three-component streamwise-averaged mean and exploits the underlying physics of the self-sustaining process. A singular value decomposition of the resolvent operator is used to obtain the mode shape for a single streamwise-varying Fourier mode. The self-interaction of the single mode is computed and used to generate an updated mean velocity input to the resolvent operator. The process is repeated until a nearly neutrally stable mean flow that self-sustains is obtained, as defined by suitable convergence criteria; the results are further verified with direct numerical simulation. The approach requires the specification of only two unknown parameters: the wave speed and amplitude of the mode. It is demonstrated that within as few as three iterations, the initial one-dimensional laminar field can be transformed into three-dimensional ECS.

Item Type:Article
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URLURL TypeDescription
Rosenberg, Kevin0000-0001-6101-3823
McKeon, Beverley J.0000-0003-4220-1583
Additional Information:© 2019 American Physical Society. Received 24 May 2019; revised manuscript received 1 July 2019; published 28 August 2019. The support of ONR under Grant No. N00014-17-1-2307 and AFOSR under Grant No. FA 9550-16-1-0361 is gratefully acknowledged.
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-17-1-2307
Air Force Office of Scientific Research (AFOSR)FA 9550-16-1-0361
Issue or Number:2
Record Number:CaltechAUTHORS:20190911-153849331
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:98589
Deposited By: Tony Diaz
Deposited On:11 Sep 2019 22:50
Last Modified:16 Nov 2021 17:40

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