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Roles of surface tension and Reynolds stresses on the finite amplitude stability of a parallel flow with a free surface

Published online by Cambridge University Press:  29 March 2006

S. P. Lin
S. P. Lin
Affiliation:
Mechanical Engineering Department, Clarkson College of Technology, Potsdam, N.Y.
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Abstract

Subcritically stable motion of long gravity waves of finite amplitude in a liquid layer flowing down an inclined plane is shown to be impossible. However, super-critically stable wave régimes for such flows are found and curves of constant wave amplitude in such régimes are obtained. The mechanism of non-linear stability is investigated by considering the energy transfer between the mean flow and the disturbances. The results obtained show that the mechanism of stability in a parallel flow with a free surface is quite different from that in a parallel flow without a free surface.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 40 , Issue 2 , 3 February 1970 , pp. 307 - 314
Copyright
© 1970 Cambridge University Press

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