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The propagation of long waves onto a continental shelf is of great interestin tsunami modeling and other applications where understanding theamplification of waves during shoaling is important. When the linearizedshallow water equations are solved with the continental shelf modeled as asharp discontinuity, the ratio of the amplitudes is given by the transmissioncoefficient. On the other hand, when the slope is very broad relative to thewavelength of the incoming wave, then amplification is governed by Green's Law,which predicts a larger amplification than the transmission coefficient, and amuch smaller amplitude reflection than given by the reflection coefficient of asharp interface. We explore the relation between these results and elucidatethe behavior in the intermediate case of a very steep continental shelf.

Shoaling on Steep Continental Slopes: Relating Transmission and Reflection Coefficients to Green's Law