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

Embargo End Date
2020-01-01

Type
Article

Authors
George, Jithin
Ketcheson, David I.
LeVeque, Randall J.

KAUST Department
Applied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Preprint Posting Date
2019-01-14

Online Publication Date
2019-09-09

Print Publication Date
2020-03

Date
2019-09-09

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.

Citation
George, J., Ketcheson, D. I., & LeVeque, R. J. (2019). Shoaling on Steep Continental Slopes: Relating Transmission and Reflection Coefficients to Green’s Law. Pure and Applied Geophysics. doi:10.1007/s00024-019-02316-y

Acknowledgements
The authors are grateful to Avi Schwarzschild for stimulating discussions in the early phase of this project.

Publisher
Springer Nature

Journal
Pure and Applied Geophysics

DOI
10.1007/s00024-019-02316-y

arXiv
1901.04148

Additional Links
http://link.springer.com/10.1007/s00024-019-02316-yhttps://repository.kaust.edu.sa/bitstream/10754/659991/1/Preprint file 1.pdf

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