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Equilibrium and travelling-wave solutions of plane Couette flow

Published online by Cambridge University Press:  29 September 2009

J. F. GIBSON ,
J. HALCROW  and
P. CVITANOVIĆ
J. F. GIBSON*
Affiliation:
School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA
J. HALCROW
Affiliation:
School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA
P. CVITANOVIĆ
Affiliation:
School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA
*
†Email address for correspondence: [email protected]
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Abstract

We present 10 new equilibrium solutions to plane Couette flow in small periodic cells at low Reynolds number Re and two new travelling-wave solutions. The solutions are continued under changes of Re and spanwise period. We provide a partial classification of the isotropy groups of plane Couette flow and show which kinds of solutions are allowed by each isotropy group. We find two complementary visualizations particularly revealing. Suitably chosen sections of their three-dimensional physical space velocity fields are helpful in developing physical intuition about coherent structures observed in low-Re turbulence. Projections of these solutions and their unstable manifolds from their ∞-dimensional state space on to suitably chosen two- or three-dimensional subspaces reveal their interrelations and the role they play in organizing turbulence in wall-bounded shear flows.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 638 , 10 November 2009 , pp. 243 - 266
Copyright
Copyright © Cambridge University Press 2009

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References

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