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.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
17 articles.
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