Journal of Fluid Mechanics

A general wave equation for waves over rippled beds

James T.  Kirby a1
a1 Coastal and Oceanographic Engineering Department, University of Florida, Gainesville, FL 32611 USA

Article author query
kirby jt   [Google Scholar] 


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 ± [infty infinity] 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.

(Published Online April 21 2006)
(Received January 2 1985)
(Revised May 17 1985)