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The interaction of deep-water gravity waves and an annular current: linear theory

Published online by Cambridge University Press:  26 April 2006

Marius Gerber
Marius Gerber
Affiliation:
Department of Applied Mathematics, Stellenbosch University, Stellenbosch, South Africa
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Abstract

The interaction of linear, steady, axisymmetric deep-water gravity waves with preexisting large-scale annular currents has been investigated. Waves originating inside the annulus as well as waves approaching the annulus from the outside were studied. Exact linear ray solutions were obtained and involve two non-dimensional parameters, a radius-angle parameter and a velocity parameter. For opposing currents the linear solutions also allow the derivation of radii at which the waves are blocked, reflected at a linear caustic or stopped by the current. Various examples of rays interacting with an annular current are presented to illustrate aspects of the solutions obtained. In particular, the behaviour of the ray solutions at blocking, reflection and stopping is investigated. Linear ray theory is shown to fail at caustics and caustic solutions are briefly discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 248 , March 1993 , pp. 153 - 172
Copyright
© 1993 Cambridge University Press

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