Shallow water models for stratified equatorial flows

TL;DR

This paper derives KdV-type shallow water models for stratified equatorial flows with arbitrary density variations, analyzing how density affects wave propagation and structure.

Contribution

It introduces new model equations accounting for depth-dependent density, extending classical models to stratified oceanic flows.

Findings

Derived explicit traveling wave solutions for stratified models

Analyzed the impact of density distribution on wave depth-structure

Provided formulas linking density profiles to wave behavior

Abstract

Our aim is to study the effect of a continuous prescribed density variation on the propagation of ocean waves. More precisely, we derive KdV-type shallow water model equations for unidirectional flows along the Equator from the full governing equations by taking into account a prescribed but arbitrary depth-dependent density distribution. In contrast to the case of constant density, we obtain for each fixed water depth a different model equation for the horizontal component of the velocity field. We derive explicit formulas for traveling wave solutions of these model equations and perform a detailed analysis of the effect of a given density distribution on the depth-structure of the corresponding traveling waves.