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Steep solitary waves in water of finite depth with constant vorticity

Published online by Cambridge University Press:  26 April 2006

J.-M. Vanden-Broeck
J.-M. Vanden-Broeck
Affiliation:
Department of Mathematics and Center for the Mathematical Sciences, University of Wisconsin-Madison, WI 53705, USA
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Abstract

Solitary waves with constant vorticity in water of finite depth are calculated numerically by a boundary integral equation method. Previous calculations are confirmed and extended. It is shown that there are branches of solutions which bifurcate from a uniform shear current. Some of these branches are characterized by a limiting configuration with a 120° angle at the crest of the wave. Other branches extend for arbitrary large values of the amplitude of the wave. The corresponding solutions ultimately approach closed regions of constant vorticity in contact with the bottom of the channel. A numerical scheme is presented to calculate directly these closed regions of constant vorticity. In addition, it is shown that there are branches of solutions which do not bifurcate from a uniform shear flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 274 , 10 September 1994 , pp. 339 - 348
Copyright
© 1994 Cambridge University Press

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