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Instability of unsteady flows or configurations Part 1. Instability of a horizontal liquid layer on an oscillating plane

Published online by Cambridge University Press:  28 March 2006

Chia-Shun Yih
Chia-Shun Yih
Affiliation:
Department of Engineering Mechanics, The University of Michigan
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Abstract

A layer of viscous liquid with a free surface is set in motion by the lower boundary moving simple-harmonically in its own plane. The stability of this motion is investigated. Since the primary flow is time-dependent, the time variable cannot be separated from at least one space variable, and a new approach must be used to investigate the problem. In this paper the stability of long waves is studied by a perturbation method which has not been applied before to problems of stability of unsteady flows, and it is found that the flow under consideration can be unstable for long waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 31 , Issue 4 , 18 March 1968 , pp. 737 - 751
Copyright
© 1968 Cambridge University Press

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