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The stability of free-surface flows with viscosity stratification

Published online by Cambridge University Press:  28 March 2006

Alex D. D. Craik  and
F. I. P. Smith
Alex D. D. Craik
Affiliation:
Department of Applied Mathematics, University of St Andrews, Fife, Scotland
F. I. P. Smith
Affiliation:
Department of Applied Mathematics, University of St Andrews, Fife, Scotland
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Abstract

The hydrodynamic stability is examined of liquids in which the viscosity varies with distance below a free surface. It is assumed that the viscosity becomes indefinitely large with distance from the surface, and that there is an ‘effective depth’ within which most of the motion occurs; but, otherwise, the viscosity distribution is arbitrary. The particular cases of wave-generation by a concurrent air flow at a horizontal liquid surface, and the stability of inclined flow under gravity are treated. It is shown that instabilities may occur which are similar to those known for thin uniform liquid films.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 34 , Issue 2 , 12 November 1968 , pp. 393 - 406
Copyright
© 1968 Cambridge University Press

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