The propagation of water waves along a channel of variable width

摘要

This paper studies surface waves in a channel withcorrugated sidewalls in water of constant depth according tolinear theory. Waves propagating along the channel encounter afinite patch of step-like corrugations in the channel walls. Themain method of solution employed is one of expansion in termsof eigenfunctions in each region and matching them at theboundaries between regions. It is found that the equationproposed by Liu in 1987 gives excellent predictions of thereflected energy flux for small-amplitude corrugations in anarrow channel (but not in more general circumstances). Forchannels wider than half a wavelength of the incident wave, atleast one higher mode will be propagating rather than evanescent.Theses higher modes can transport energy away from theirregularities, thus invalidating approaches to the problem whichignore them. In some circumstances, an incident wave may betotally reflected from just a single indentation in the channel wall.The technique is also used to study channels with continuously -varying wall profiles by approximating such profiles by a series of steps.