The Propagation of Water Waves along a Channel with a Corrugated Sidewall

This paper studies surface gravity waves in a channel with corrugated sidewalls in water of constant depth according to linear theory. Waves propagating along the channel encounter a nite patch of step-like corrugations in one of the channel walls. The method of solution employed is one of expansion in terms of eigenfunctions in each region and matching at the boundaries between regions. It is found that the theory proposed by Liu in 1987 gives excellent predictions of the reeected energy ux for small-amplitude corrugations in a narrow channel but not in more general circumstances. For channels wider than half a wavelength of the incident wave, at least one higher mode will be propagating rather than evanescent. These higher modes can transport energy away from the irregularities thus invalidating approaches to the problem which ignore them. In some circumstances, an incident wave may be totally reeected from just a single indentation in the channel wall.