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Hydro-acoustic frequencies of the weakly compressible mild-slope equation

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journal contribution
posted on 2016-11-23, 11:40 authored by Emiliano Renzi
We present a novel analytical solution for hydro-acoustic waves in a weakly compressible fluid over a slowly varying bottom. Application of a multiple-scale perturbation technique and matched asymptotic analysis leads to a uniform analytical solution of the depth-averaged governing equations in three dimensions. We show that the slow depth variation plays a leading-order effect on the evolution of the normal mode amplitude and direction. This dynamics is much richer than the two-dimensional limit analysed in previous studies. For tsunamigenic disturbances, we show that the hydro-acoustic wave field is made up by longshore trapped and offshore propagating components, which were not explicated in previous work. For a plane beach, we find an exact analytical solution of the model equation in terms of integrals of Bessel functions. Our model offers a physical insight into the evolution of hydro-acoustic waves of interest for the design of tsunami early warning systems.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Journal of Fluid Mechanics

Volume

812

Pages

5 - 25

Citation

RENZI, E., 2016. Hydro-acoustic frequencies of the weakly compressible mild-slope equation. Journal of Fluid Mechanics, 812, pp. 5-25.

Publisher

© Cambridge University Press

Version

  • AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Acceptance date

2016-11-06

Publication date

2016-12-22

Notes

This paper was accepted for publication in the journal Journal of Fluid Mechanics and the definitive published version is available at https://doi.org/10.1017/jfm.2016.791

ISSN

0022-1120

eISSN

1469-7645

Language

  • en

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