Shallow water models for stratified equatorial flows
Fluid Dynamics
2018-10-29 v1 Analysis of PDEs
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.
Cite
@article{arxiv.1810.11450,
title = {Shallow water models for stratified equatorial flows},
author = {Anna Geyer and Ronald Quirchmayr},
journal= {arXiv preprint arXiv:1810.11450},
year = {2018}
}