Shallow water models for stratified equatorial flows Article Swipe

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Korteweg–de Vries equation Constant (computer programming) Shallow water equations Density contrast Waves and shallow water Mathematical analysis Equator Distribution (mathematics) Mathematics Mechanics Component (thermodynamics) Geology Geometry Physics Nonlinear system Geodesy Oceanography Quantum mechanics Latitude Computer science Programming language Astronomy Thermodynamics

Anna Geyer , Ronald Quirchmayr ·

YOU? · · 2019 · Open Access · · DOI: https://doi.org/10.3934/dcds.2019186 · OA: W2898089756

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.