Solitary Wave Solution of Flat Surface Internal Geophysical Waves with Vorticity

TL;DR

This paper derives a solitary wave solution for internal geophysical waves with vorticity in a fluid system, using Hamiltonian dynamics and KdV approximation, contributing to understanding wave behavior in stratified fluids.

Contribution

It introduces a novel solitary wave solution for internal waves with vorticity, extending Hamiltonian and KdV frameworks to this context.

Findings

Derivation of a solitary wave solution for internal waves with vorticity.

Extension of KdV approximation to systems with depth-dependent currents.

Insight into wave dynamics in stratified, rotating fluid systems.

Abstract

A fluid system bounded by a flat bottom and a flat surface with an internal wave and depth-dependent current is considered. The Hamiltonian of the system is presented and the dynamics of the system are discussed. A long-wave regime is then considered and extended to produce a KdV approximation. Finally, a solitary wave solution is obtained.