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On the instability of wave-catalysed longitudinal vortices in strong shear

Published online by Cambridge University Press:  26 April 2006

W.R.C. Phillips  and
Z. Wu
W.R.C. Phillips
Affiliation:
Department of Mechanical and Aeronautical Engineering, Box 5725, Clarkson University, Potsdam, NY 13699-5725, USA
Z. Wu
Affiliation:
Department of Mechanical and Aeronautical Engineering, Box 5725, Clarkson University, Potsdam, NY 13699-5725, USA
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Abstract

The inviscid instability of O(ϵ) two-dimensional periodic flows to spanwise-periodic longitudinal vortex modes in parallel O(1) shear flows is considered. In such cases, not only is the effect of fluctuations upon the mean state important but also the influence of the developing mean flow on the fluctuating part of the motion. The former is described by a generalized Lagrangian-mean formulation; the latter by a modified Rayleigh equation. Of specific interest is whether the spanwise distortion of the wave field feeds back to enhance or inhibit instability to longitudinal vortex form. Two cases are considered in detail: uniform shear between wavy walls and non-uniform shear beneath free-surface waves. In both cases wave distortion acts to inhibit, and in some circumstances curtail, instability for all but the shortest waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 272 , 10 August 1994 , pp. 235 - 254
Copyright
Copyright © Cambridge University Press 1994

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