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Finite-amplitude instability of parallel shear flows

Published online by Cambridge University Press:  28 March 2006

W. C. Reynolds  and
Merle C. Potter
W. C. Reynolds
Affiliation:
Department of Mechanical Engineering, Stanford University
Merle C. Potter
Affiliation:
Mechanical Engineering Department, Michigan State University
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Abstract

A formal expansion method for analysis of the non-linear development of an oblique wave in a parallel flow is presented. The present approach constitutes an extension and modification of the method of Stuart and Watson. Results are obtained for plane Poiseuille flow, and for a combination of plane Poiseuille and plane Couette flow. The Poiseuille flow exhibits finite-amplitude subcritical instability, and relatively weak but finite disturbances markedly reduce the critical Reynolds number. The combined flow, which becomes stable to infinitesimal disturbances at all Reynolds numbers when the Couette component is sufficiently great, remains unstable to finite disturbances.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 27 , Issue 3 , 24 February 1967 , pp. 465 - 492
Copyright
© 1967 Cambridge University Press

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