On the dynamics of internal waves propagating in stratified media of a variable depth: exact and asymptotic solutions

TL;DR

This paper derives asymptotic solutions to describe the far field of internal gravity waves in stratified media with variable depth, providing a qualitative understanding where numerical methods fall short.

Contribution

The paper introduces asymptotic models for internal wave dynamics in stratified media with variable bottom topography, extending analytical understanding beyond specific cases.

Findings

Derived asymptotic solutions for internal wave far field

Provided qualitative descriptions where numerical methods are inadequate

Enhanced understanding of wave behavior in variable-depth stratified media

Abstract

The dynamics of internal waves in stratified media, such as the ocean or atmosphere, is highly dependent on the topography of their floor. A closed-form analytical solution can be derived only in cases when the water distribution density and the shape of the floor are modeled with specific functions. In a general case when the characteristics of stratified media and the boundary conditions are arbitrary, the dynamics of internal waves can be only approximated with numerical methods. However, numerical solutions do not describe the wave field qualitatively. At the same time, the need for a qualitative analysis of the far field of internal waves arises in studies applying remote sensing methods in space-based radar applications. In this case, the dynamics of internal waves can be described using asymptotic models. In this paper, we derive asymptotic solutions to the problem of characterizing the far field of internal gravity waves propagating in a stratified medium with a smoothly varying floor.