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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. https://resolver.caltech.edu/CaltechAUTHORS:20190911-153849331

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Abstract

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
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/physreve.100.021101DOIArticle
ORCID:
AuthorORCID
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.
Group:GALCIT
Funders:
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
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190911-153849331
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:98589
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:11 Sep 2019 22:50
Last Modified:03 Oct 2019 21:42

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