Shallow water models for stratified equatorial flows

Journal article (2019)

Authors

A. Geyer Mathematical Physics - EEMCS
Ronald Quirchmayr KTH Royal Institute of Technology
Research Group
Mathematical Physics (EEMCS) (TU Delft)
Continuous density stratification Equatorial shallow water equations Explicit traveling wave solutions
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Published Date

2019

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Mathematical Physics

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.