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A streamwise constant model of turbulence in plane Couette flow

Gayme, D. F. and McKeon, B. J. and Papachristodoulou, A. and Bamieh, B. and Doyle, J. C. (2010) A streamwise constant model of turbulence in plane Couette flow. Journal of Fluid Mechanics, 665 . pp. 99-119. ISSN 0022-1120. http://resolver.caltech.edu/CaltechAUTHORS:20110131-095901289

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Abstract

Streamwise and quasi-streamwise elongated structures have been shown to play a significant role in turbulent shear flows. We model the mean behaviour of fully turbulent plane Couette flow using a streamwise constant projection of the Navier–Stokes equations. This results in a two-dimensional three-velocity-component (2D/3C) model. We first use a steady-state version of the model to demonstrate that its nonlinear coupling provides the mathematical mechanism that shapes the turbulent velocity profile. Simulations of the 2D/3C model under small-amplitude Gaussian forcing of the cross-stream components are compared to direct numerical simulation (DNS) data. The results indicate that a streamwise constant projection of the Navier–Stokes equations captures salient features of fully turbulent plane Couette flow at low Reynolds numbers. A systems-theoretic approach is used to demonstrate the presence of large input–output amplification through the forced 2D/3C model. It is this amplification coupled with the appropriate nonlinearity that enables the 2D/3C model to generate turbulent behaviour under the small-amplitude forcing employed in this study.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1017/S0022112010003861DOIArticle
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=7930491PublisherArticle
https://arxiv.org/abs/1001.0782arXivDiscussion Paper
ORCID:
AuthorORCID
McKeon, B. J.0000-0003-4220-1583
Doyle, J. C.0000-0002-1828-2486
Additional Information:© 2010 Cambridge University Press. Received 21 October 2009; revised 14 July 2010; accepted 14 July 2010; first published online 19 October 2010. The authors would like to thank H. Kawamura and T. Tsukahara for providing us with their DNS data. This research is sponsored in part through a grant from the Boeing Corporation. B.J.M. gratefully acknowledges support from NSF-CAREER award number 0747672 (programme managers W. W. Schultz and H. H. Winter).
Group:GALCIT
Funders:
Funding AgencyGrant Number
Boeing CorporationUNSPECIFIED
NSFCBET-0747672
Subject Keywords:nonlinear dynamical systems, turbulence modelling, turbulent boundary layers
Record Number:CaltechAUTHORS:20110131-095901289
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20110131-095901289
Official Citation:D. F. GAYME, B. J. McKEON, A. PAPACHRISTODOULOU, B. BAMIEH and J. C. DOYLE (2010). A streamwise constant model of turbulence in plane Couette flow. Journal of Fluid Mechanics, 665, pp 99-119 doi:10.1017/S0022112010003861
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:21931
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:11 Feb 2011 19:07
Last Modified:27 Aug 2018 17:27

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