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The damping of capillary–gravity waves at a rigid boundary

Published online by Cambridge University Press:  21 April 2006

L. M. Hocking
L. M. Hocking
Affiliation:
Department of Mathematics, University College London, Gower Street. London WC1E 6BT, UK
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Abstract

The frequency and damping rate of surface capillary-gravity waves in a bounded region depend on the conditions imposed where the free surface makes contact with the boundary. Extreme cases are when the free surface meets the boundary orthogonally, as in the case of pure gravity waves, and when the contact line remains fixed throughout the motion. An edge condition that models to some extent the dynamics associated with moving contact lines, but not contact-angle hysteresis, is given by making the slope of the free surface at contact proportional to its velocity. This model, which includes the two extreme cases, is used to obtain the frequency and damping rate of a standing wave between two parallel vertical walls. The effect of viscosity in the boundary layers on the walls is included and it is shown that the dissipation associated with the surface forces can exceed that produced by viscosity. The results are compared with those obtained from a number of experimental investigations, in which damping rates too large to be attributed to viscous action have been measured.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 179 , June 1987 , pp. 253 - 266
Copyright
© 1987 Cambridge University Press

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