Propagation of acoustic waves near an ocean surface with mean flow inhomogeneities

Abstract

There is considerable interest in the model of underwater sound propagation in a moving-stratified ocean as it has long been established that variations in current speed have significant effects on the propagation of acoustic waves. This is due to the fact that these variations modify the sound-speed structure. This paper describes a mathematically rigorous method to study the propagation of acoustic waves in a vertically stratified ocean with a mean flow. Much of the significant theoretical work in this field makes use of a high frequency approximation and the so-called plane-wave ansatz. In this classical method, one substitutes the ansatz into the governing wave equation in order to determine an approximate solution. The first-order approximation leads to an eikonal equation that defines the ‘‘rays’’ and the second-order approximation leads to a transport equation that gives the wave amplitude. However, a different approach is used in this paper. It is demonstrated that the acoustic pressure can be represented by a twofold Fourier integral. The sound pressure is then estimated asymptotically by the method of stationary phase. The solution is particularly useful to provide a better physical understanding of the problem at much reduced computational cost.