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A general wave equation for waves over rippled beds

Published online by Cambridge University Press:  21 April 2006

James T. Kirby
Affiliation:
Coastal and Oceanographic Engineering Department, University of Florida, Gainesville, FL 32611 USA

Abstract

A time-dependent extension of the reduced wave equation of Berkhoff is developed for the case of waves propagating over a bed consisting of ripples superimposed on an otherwise slowly varying mean depth which satisfies the mild-slope assumption. The ripples are assumed to have wavelengths on the order of the surface wavelength but amplitudes which scale as a small parameter along with the bottom slope. The theory is verified by showing that it reduces to the case of plane waves propagating over a patch of sinusoidal ripples, which vary in one direction and extend to ± ∞ in the transverse direction, studied recently by Davies & Heathershaw and Mei. We then formulate and use coupled parabolic equations to study propagation over patches of arbitrary form in order to study wave reflection.

Type
Research Article
Copyright
© 1986 Cambridge University Press

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References

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