Three‐layer flows in the shallow water limit

De Melo Virissimo, Francisco ORCID:; Milewski, Paul A.. 2019 Three‐layer flows in the shallow water limit [in special issue: Special Issue: Nonlinear Waves in Fluids: in Honor of Roger Grimshaw on the Occasion of his 80th Birthday, Part II] Studies in Applied Mathematics, 142 (4).

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We formulate and discuss the shallow water limit dynamics of the layered flow with three layers of immiscible fluids of different densities bounded above and below by horizontal walls. We obtain a resulting system of four equations, which may be nonlocal in the non‐Boussinesq case. We provide a systematic way to pass to the Boussinesq limit, and then study those equations, which are first‐order PDEs of mixed type, more carefully. We show that in a symmetric case the solutions remain on an invariant surface and using simple waves we illustrate that this is not the case for nonsymmetric cases. Reduced models consisting of systems of two equations are also proposed and compared to the full system.

Item Type: Publication - Article
Digital Object Identifier (DOI):
ISSN: 0022-2526
Date made live: 02 Mar 2020 11:54 +0 (UTC)

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