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Wave action on currents with vorticity

Published online by Cambridge University Press:  10 May 1999

BENJAMIN S. WHITE
BENJAMIN S. WHITE
Affiliation:
Exxon Research and Engineering Co., Route 22 East, Annandale, NJ 08801, USA
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Abstract

The interaction of waves on deep water with spatially varying currents may be described by a ray theory, with the wave amplitudes determined by the principle of conservation of wave action (CWA). However, all previous deep water derivations of CWA are restricted to the case of an irrotational current. In this paper, both the ray theory and CWA are derived by a WKB method without the assumption of irrotationality. Also derived is a new equation for a spatially varying phase shift which is not predicted by the usual ray theory, and which, in general, displaces the positions of the wave crests by a distance on the order of a wavelength. This phase shift, which is caused by variations of the current velocity with depth, vanishes in the irrotational case, and so is in accord with the irrotational theory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 386 , 10 May 1999 , pp. 329 - 344
Copyright
© 1999 Cambridge University Press

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