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

Published online by Cambridge University Press:  22 December 2016

Emiliano Renzi
Emiliano Renzi*
Affiliation:
Department of Mathematical Sciences, Loughborough University, Loughborough, Leics LE11 3TU, UK
*
†Email address for correspondence: E.Renzi@lboro.ac.uk
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Abstract

We present a novel analytical solution for hydro-acoustic waves in a weakly compressible fluid flow 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 has 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.

JFM classification

Compressible Flows: Compressible Flows Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 812 , 10 February 2017 , pp. 5 - 25
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Copyright
© 2016 Cambridge University Press 

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