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.
机构:
Department of Mathematical Sciences, Univesity of Bath, Bath,BA2 7AY, United KingdomDepartment of Mathematical Sciences, Univesity of Bath, Bath,BA2 7AY, United Kingdom
Doak, A.
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机构:
Barros, R.
Milewski, P.A.
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机构:
Department of Mathematical Sciences, Univesity of Bath, Bath,BA2 7AY, United KingdomDepartment of Mathematical Sciences, Univesity of Bath, Bath,BA2 7AY, United Kingdom
机构:
Hong Kong Univ Sci & Technol, Dept Civil & Environm Engn, Kowloon, Hong Kong, Peoples R ChinaHong Kong Univ Sci & Technol, Dept Civil & Environm Engn, Kowloon, Hong Kong, Peoples R China
Ng, Charles W. W.
Coo, Jason L.
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机构:
Hong Kong Univ Sci & Technol, Dept Civil & Environm Engn, Kowloon, Hong Kong, Peoples R ChinaHong Kong Univ Sci & Technol, Dept Civil & Environm Engn, Kowloon, Hong Kong, Peoples R China
Coo, Jason L.
Chen, Zhong Kui
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机构:
Hong Kong Univ Sci & Technol, Dept Civil & Environm Engn, Kowloon, Hong Kong, Peoples R ChinaHong Kong Univ Sci & Technol, Dept Civil & Environm Engn, Kowloon, Hong Kong, Peoples R China
Chen, Zhong Kui
Chen, Rui
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机构:
Harbin Inst Technol, Shenzhen Key Lab Urban & Civil Engn Disaster Prev, Shenzhen Grad Sch, Shenzhen 518055, Peoples R ChinaHong Kong Univ Sci & Technol, Dept Civil & Environm Engn, Kowloon, Hong Kong, Peoples R China