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arXiv · 1507.02215

The multilayer shallow water system in the limit of small density contrast

Vincent Duchêne
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Abstract

We study the inviscid multilayer Saint-Venant (or shallow-water) system in the limit of small density contrast. We show that, under reasonable hyperbolicity conditions on the flow and a smallness assumption on the initial surface deformation, the system is well-posed on a large time interval, despite the singular limit. By studying the asymptotic limit, we provide a rigorous justification of the widely used rigid-lid and Boussinesq approximations for multilayered shallow water flows. The asymptotic behaviour is similar to that of the incompressible limit for Euler equations, in the sense that there exists a small initial layer in time for ill-prepared initial data, accounting for rapidly propagating "acoustic" waves (here, the so-called barotropic mode) which interact only weakly with the "incompressible" component (here, baroclinic).

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Vincent Duchêne. 2015-07-08. The multilayer shallow water system in the limit of small density contrast. https://doi.org/10.3233/asy-161366

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