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Title: Hydro-acoustic frequencies of the weakly compressible mild-slope equation
Authors: Renzi, Emiliano
Issue Date: 2016
Publisher: © Cambridge University Press
Citation: RENZI, E., 2016. Hydro-acoustic frequencies of the weakly compressible mild-slope equation. Journal of Fluid Mechanics, 812, pp. 5-25.
Abstract: 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.
Description: 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
Version: Accepted for publication
DOI: 10.1017/jfm.2016.791
URI: https://dspace.lboro.ac.uk/2134/23262
Publisher Link: https://doi.org/10.1017/jfm.2016.791
ISSN: 0022-1120
Appears in Collections:Published Articles (Maths)

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