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

by J. D. George, D. I. Ketcheson, and R. J. LeVeque,
*Pure and Applied Geophysics*, 2019.
DOI
10.1007/s00024-019-02316-y

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

**Preprint:**
https://arxiv.org/abs/1901.04148

Journal: article (requires subscription) ... Read-only free version

**bibtex entry:**

@misc{GeorgeKetchesonLeVeque2019a, author="J. D. George and R. J. LeVeque and D. I. Ketcheson", title="Shoaling on Steep Continental Slopes: Relating Transmission and Reflection Coefficients to {Green's Law}", howpublished = "arXiv:1901.04148", year="2019" }