Internal Gravity Waves in a Stratified Fluid with Smoothly Varying Bottom

TL;DR

This paper develops asymptotic solutions for internal gravity waves generated by a moving source in a stratified fluid with a smoothly varying bottom, analyzing wave behavior near fronts and away from them.

Contribution

It provides new asymptotic solutions for internal waves in complex stratified environments with variable bottom topography, including explicit formulas for rays and phase structures.

Findings

Exact analytic expressions for rays in specific bottom and stratification models

Analysis of phase structure of the wave field

Wave amplitude determined by energy conservation law

Abstract

The far field asymptotic of internal waves is constructed for the case when a point source of mass moves in a layer of arbitrarily stratified fluid with slowly varying bottom. The solutions obtained describe the far field both near the wave fronts of each individual mode and away from the wave fronts and are expansions in Airy or Fresnel waves with the argument determined from the solution of the corresponding eikonal equation. The amplitude of the wave field is determined from the energy conservation law along the ray tube. For model distributions of the bottom shape and the stratification describing the typical pattern of the ocean shelf exact analytic expressions are obtained for the rays, and the properties of the phase structure of the wave field are analyzed.