Asymptotics of Far Fields of Internal Gravity Waves in Stratified Media of Variable Depth

In this work, the wave dynamics of far fields of internal gravity waves in stratified media of variable depth is studied. One of the most difficult questions is considered arising in investigating the wave dynamics by means of the geometric optics methods: the problem of constructing the asymptotics near singular spatial curves and surfaces—caustics. The asymptotic representations built in this work in the most general form allow describing the far field of internal gravity waves excited by a source moving over a slowly changing bottom. The uniform asymptotic expressions of the solution are obtained that reflect the main peculiarities of the wave fields near caustics and wave fronts. Universal character of the proposed asymptotic methods and approaches allows efficiently computing the wave fields at large distances from the source moving in a stratified medium of variable depth. The obtained analytical results enable analyzing the wave patterns in their entirety, which is important for both the correct formulation of the mathematical models of wave dynamics and estimation calculations at field measurements of wave fields in the ocean.