Three-layer flows in the shallow water limit

Francisco de Melo Viríssimo, Paul A. Milewski

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3 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)487-512
Number of pages26
JournalStudies in Applied Mathematics
Issue number4
StatePublished - May 2019

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

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