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