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Shear-flow instability due to a wall and a viscosity discontinuity at the interface

Published online by Cambridge University Press:  21 April 2006

A. P. Hooper  and
W. G. C. Boyd
A. P. Hooper
Affiliation:
Department of Mathematics, University of Bristol, Bristol BS8 1TW, UK
W. G. C. Boyd
Affiliation:
Department of Mathematics, University of Bristol, Bristol BS8 1TW, UK
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Abstract

Consider the Couette flow of two superposed fluids of different viscosity with the depth of the lower fluid bounded by a wall and the interface while the depth of the upper fluid is unbounded. The linear instability of this flow configuration is studied at all values of flow Reynolds number and disturbance wavelength using both asymptotic and numerical methods. Three distinct forms of instability are found which are dependent on the magnitude of two dimensionless parameters β and (α R)1/3, where β is a dimensionless wavenumber measured on a viscous lengthscale, α is a dimensionless wavenumber measured on the scale of the depth of the lower fluid and R is the Reynolds number of the lower fluid. At large β there is the short-wave instability found previously by Hooper & Boyd (1983). At small β and small (αR)1/3 there is the long-wave instability first discovered by Yih. At small β and large (αR)1/3 there is a new type of instability which arises only if the kinematic viscosity of the lower bounded fluid is less than the kinematic viscosity of the upper fluid.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 179 , June 1987 , pp. 201 - 225
Copyright
© 1987 Cambridge University Press

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