On the effects of irregular boundaries in finite difference models

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Abstract
Propagation of periodic waves in the vicinity of irregular saw‐tooth shaped boundary in finite difference models is investigated. The reflection of an incoming wave from a single saw‐tooth boundary is found to be accompanied by a phase shift. It is shown that any wave mode propagating along such a boundary is trapped and decays in the direction normal to the boundary. A wave propagating along a channel with saw‐tooth shaped lateral boundaries is influenced by the trapped waves, which leads to a reduction of the phase velocity. Phase velocities obtained from the present normal mode analysis are compared to velocities in numerical experiments. The agreement is excellent.

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