Three-layer flows in the shallow water limit

被引:4
|
作者
Virissimo, Francisco de Melo [1 ]
Milewski, Paul A. [1 ]
机构
[1] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England
基金
巴西圣保罗研究基金会;
关键词
hyperbolic systems; interfacial waves; nonlinear waves; stratified flows; LONG WAVES;
D O I
10.1111/sapm.12266
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页码:487 / 512
页数:26
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