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Parametric solutions for breaking waves

Published online by Cambridge University Press:  20 April 2006

M. S. Longuet-Higgins
M. S. Longuet-Higgins
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge, England, and Institute of Oceanographic Sciences, Wormley, Surrey
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Abstract

Time-dependent flows such as occur in breaking surface waves are often most con- veniently described in parametric form, with the coordinate z and velocity potential χ each expressed in terms of a third complex variable ω and the time t.

In this paper we discuss some interesting flows given in terms of elementary functions of ω and t. Included are the Stokes 120° corner flow, the 45° rotor or rotating wedge, and a decelerated upwelling flow, with an exactly plane surface.

Lastly it is shown that a class of cubic flows, which are related to the plane upwelling flow just mentioned, has a free surface that corresponds with remarkable accuracy to the forward face of an overturning, or plunging, breaker.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 121 , August 1982 , pp. 403 - 424
Copyright
© 1982 Cambridge University Press

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