Internal gravity waves in a stratified medium of non-uniform depth

TL;DR

This paper develops an asymptotic method to reconstruct internal gravity wave packets in a stratified ocean with non-uniform depth, using wave modes and a modified ray technique for better approximation.

Contribution

It introduces a uniform asymptotic form for internal gravity waves in variable-depth stratified media using a non-integral series expansion and a modified geometrical optics approach.

Findings

Derived a uniform asymptotic solution for wave fields

Proposed a modified space-time ray method

Expressed wave packets via Airy functions based on local dispersion

Abstract

The problem of reconstructing non-harmonic internal gravity wave packets generated by a source moving in a stratified ocean is considered. The uniform asymptotic form of the internal gravity waves field generated by a source moving above the smoothly varying floor is constructed. The solution is proposed in terms of wave modes, propagating independently at the adiabatic approximation, and described as a non-integral degree series of a small parameter characterizing the stratified medium. A specific form of the wave packets, which can be parameterized in terms of model functions (Airy functions), depends on a local behavior of the dispersion curves of individual wave mode. A modified space-time ray method was proposed, which belongs to the class of geometrical optics methods. The key point of the proposed technique is the possibility to derive the asymptotic representation of the solution in terms of a non-integral degree series of the some small parameter.