Abstract

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 non-local 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 non-symmetric cases. Reduced models consisting of systems of 2 equations are also proposed and compared to the full system.
Original languageEnglish
Pages (from-to)487-512
Number of pages26
JournalStudies in Applied Mathematics
Volume142
Issue number4
Early online date19 Mar 2019
DOIs
Publication statusPublished - 1 May 2019

Keywords

  • hyperbolic systems
  • interfacial waves
  • nonlinear waves
  • stratified flows

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Three-layer flows in the shallow water limit. / de Melo Viríssimo, Francisco; Milewski, Paul.

In: Studies in Applied Mathematics, Vol. 142, No. 4, 01.05.2019, p. 487-512.

Research output: Contribution to journalArticle

de Melo Viríssimo, Francisco ; Milewski, Paul. / Three-layer flows in the shallow water limit. In: Studies in Applied Mathematics. 2019 ; Vol. 142, No. 4. pp. 487-512.
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