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Amplification and nonlinear mechanisms in plane Couette flow

Gayme, Dennice F. and McKeon, Beverley J. and Bamieh, Bassam and Papachristodoulou, Antonis and Doyle, John C. (2011) Amplification and nonlinear mechanisms in plane Couette flow. Physics of Fluids, 23 (6). 065108 . ISSN 1070-6631.

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We study the input-output response of a streamwise constant projection of the Navier-Stokes equations for plane Couette flow, the so-called 2D/3C model. Study of a streamwise constant model is motivated by numerical and experimental observations that suggest the prevalence and importance of streamwise and quasi-streamwise elongated structures. Periodic spanwise/wall-normal (z–y) plane stream functions are used as input to develop a forced 2D/3C streamwise velocity field that is qualitatively similar to a fully turbulent spatial field of direct numerical simulation data. The input-output response associated with the 2D/3C nonlinear coupling is used to estimate the energy optimal spanwise wavelength over a range of Reynolds numbers. The results of the input-output analysis agree with previous studies of the linearized Navier-Stokes equations. The optimal energy corresponds to minimal nonlinear coupling. On the other hand, the nature of the forced 2D/3C streamwise velocity field provides evidence that the nonlinear coupling in the 2D/3C model is responsible for creating the well known characteristic “S” shaped turbulent velocity profile. This indicates that there is an important tradeoff between energy amplification, which is primarily linear, and the seemingly nonlinear momentum transfer mechanism that produces a turbulent-like mean profile.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
McKeon, Beverley J.0000-0003-4220-1583
Bamieh, Bassam0000-0001-9237-4613
Doyle, John C.0000-0002-1828-2486
Additional Information:© 2011 American Institute of Physics. Received 18 November 2010; accepted 17 May 2011; published online 17 June 2011. The authors would like to thank H. Kawamura and T. Tsukahara for providing them with their DNS data. This research is partially supported by AFOSR (FA9550-08-1-0043). B.J.M. gratefully acknowledges support from NSFCAREER Award No. 0747672 (program managers W. W. Schultz and H. H. Winter).
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-08-1-0043
Subject Keywords:Couette flow; flow simulation; Navier-Stokes equations; turbulence
Issue or Number:6
Classification Code:PACS: 47.15.-x; 47.27.E-;
Record Number:CaltechAUTHORS:20110722-112408053
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:24507
Deposited By: Jason Perez
Deposited On:22 Jul 2011 20:28
Last Modified:09 Mar 2020 13:18

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