Abstract
Steady-state wave solutions are obtained in closed form for two simple coastal geometries. The first model consists of two regions of constant depth separated by a step, and the second model consists of a constantdepth region joined by a step to a region in which the mean depth decreases linearly to a value of zero at the shore line. The step, which is used to model a continental shelf, can create resonance and large wave amplifications in both cases, but amplifications are found to be much greater for the second model. Furthermore, peak amplifications at resonance are found to not change with incident wave frequency for the first model but to increase with wave frequency for the second model. Finally, since wave amplifications in the second model depend very strongly on incident wave frequencies, periods are calculated for waves near the leading edge of a tsunami wave train moving through water of constant depth.
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