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Shear-flow instability at the interface between two viscous fluids

Published online by Cambridge University Press:  20 April 2006

A. P. Hooper  and
W. G. C. Boyd
A. P. Hooper
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW Present address: Department of Mathematics, University of Melbourne, Parkville, Victoria 3052, Australia.
W. G. C. Boyd
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW
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Abstract

We consider the linear stability of the cocurrent flow of two fluids of different viscosity in an infinite region (the viscous analogue of the classical Kelvin-Helmholtz problem). Attention is confined to the simplest case, Couette flow, and we solve the problem using both numerical and asymptotic techniques. We find that the flow is always unstable (in the absence of surface tension). The instability arises at the interface between the two fluids and occurs for short wavelengths, when viscosity rather than inertia is the dominant physical effect.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 128 , March 1983 , pp. 507 - 528
Copyright
© 1983 Cambridge University Press

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