The propagation of water waves along a channel of variable width

This paper studies surface waves in a channel with corrugated sidewalls in water of constant depth according to linear theory. Waves propagating along the channel encounter a finite patch of step-like corrugations in the chan nel walls. The main method of solution employed is one of expansion in term s of eigenfunctions in each region and matching them at the boundaries betw een regions. It is found that the equation proposed by Liu in 1987 gives ex cellent predictions of the reflected energy flux for small-amplitude corrug ations in a narrow channel (but not in more general circumstances). For cha nnels wider than half a wavelength of the incident wave, at least one highe r mode will be propagating rather than evanescent. These higher modes can t ransport energy away from the irregularities, thus invalidating approaches to the problem which ignore them. In some circumstances, an incident wave m ay be totally reflected from just a single indentation in the channel wall. The technique is also used to study channels with continuously-varying wal l profiles by approximating such profiles by a series of steps. (C) 1999 El sevier Science Ltd. All rights reserved.