On multisolitonic decay behavior of internal gravity waves

TL;DR

This paper investigates the multisoliton decay behavior of internal gravity waves, combining analytical and numerical methods to model wave dynamics and interactions in stratified fluids.

Contribution

It introduces a comprehensive approach to modeling internal wave behavior using Sturm-Liouville eigenfunctions and coupled Korteweg-de Vries systems, with validation against experimental data.

Findings

Multisoliton interactions can increase wave scale and complexity.

Numerical solutions match experimental stratification profiles.

The scheme is stable and convergent for realistic internal wave problems.

Abstract

We claim that changes of scales and fine-structure could increase from multisoliton behavior of internal waves dynamics and, further, in the so-called "wave mixing". We consider initial-boundary problems for Euler equations with a stratified background state that is valid for internal water waves. The solution of the problem we search in the waveguide mode representation for a current function. The orthogonal eigenfunctions describe a vertical shape of the internal wave modes and satisfy a Sturm-Liouville problem for the vertical variable. The Cauchy problem is solved for initial conditions with realistic geometry and magnitude. We choose the geometry and dimensions of the McEwan experiment with the stratification of constant buoyancy frequency. The horizontal profile is defined by numerical solutions of a coupled Korteweg-de Vries system. The numerical scheme is proved to be convergent, stable and tested by means of explicit solutions for integrable case of the system. Together with the solution of the Sturm-Liouville problem it gives the complete internal waves profile.