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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
James T. Kirby
Affiliation:
Coastal and Oceanographic Engineering Department, University of Florida, Gainesville, FL 32611 USA
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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
Information
Journal of Fluid Mechanics , Volume 162 , January 1986 , pp. 171 - 186
Copyright
© 1986 Cambridge University Press

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References

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