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A streamwise constant model of turbulence in plane Couette flow

Published online by Cambridge University Press:  19 October 2010

D. F. GAYME ,
B. J. McKEON ,
A. PAPACHRISTODOULOU ,
B. BAMIEH  and
J. C. DOYLE
D. F. GAYME*
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
B. J. McKEON
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
A. PAPACHRISTODOULOU
Affiliation:
Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK
B. BAMIEH
Affiliation:
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
J. C. DOYLE
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Nonlinear Dynamical Systems: Nonlinear Dynamical Systems Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 665 , 25 December 2010 , pp. 99 - 119
Copyright
Copyright © Cambridge University Press 2010

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