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A parabolic equation for the combined refraction–diffraction of Stokes waves by mildly varying topography

Published online by Cambridge University Press:  20 April 2006

James T. Kirby  and
Robert A. Dalrymple
James T. Kirby
Affiliation:
Department of Civil Engineering, University of Delaware, Newark, DE 19711 Present address: Marine Sciences Research Center, State University of New York, Stony Brook, New York 11794.
Robert A. Dalrymple
Affiliation:
Department of Civil Engineering, University of Delaware, Newark, DE 19711
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Abstract

A parabolic equation governing the leading-order amplitude for a forward-scattered Stokes wave is derived using a multiple-scale perturbation method, and the connection between the linearized version and a previously derived approximation of the linear mild slope equation is investigated. Two examples are studied numerically for the situation where linear refraction theory leads to caustics, and the nonlinear model is shown to predict the development of wave-jump conditions and significant reductions in amplitude in the vicinity of caustics.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 136 , November 1983 , pp. 453 - 466
Copyright
© 1983 Cambridge University Press

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