Renzi, Emiliano Hydro-acoustic frequencies of the weakly compressible mild-slope equation 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. untagged;Mathematical Sciences not elsewhere classified 2016-11-23
    https://repository.lboro.ac.uk/articles/journal_contribution/Hydro-acoustic_frequencies_of_the_weakly_compressible_mild-slope_equation/9388682