Derivation of a non-hydrostatic shallow water model; Comparison with Saint-Venant and Boussinesq systems

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September 2008, 10(4): 733-759. doi: 10.3934/dcdsb.2008.10.733

Derivation of a non-hydrostatic shallow water model; Comparison with Saint-Venant and Boussinesq systems

Marie-Odile Bristeau ^1, and Jacques Sainte-Marie ^2,

1.	INRIA Roquencourt, B.P. 105, 78153 Le Chesnay Cedex, France
2.	Saint-Venant Laboratory, 6 quai Watier, 78400 Chatou and INRIA Rocquencourt, B.P. 105, 78153 Le Chesnay Cedex, France

Received April 2007 Revised June 2008 Published August 2008

Abstract
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From the free surface Navier-Stokes system, we derive the non-hydrostatic Saint-Venant system for the shallow waters including friction and viscosity. Based on an asymptotic analysis, the derivation leads to two formulations of growing complexity depending on the level of approximation chosen for the fluid pressure. The obtained models rely on formal estimates and are compared with the Boussinesq models.

Keywords: Boussinesq equations, Saint-Venant equations, Dispersive terms, Navier-Stokes equations, Free surface, Asymptotic analysis..

Mathematics Subject Classification: Primary: 35Q30, 35Q35; Secondary: 76D0.

Citation: Marie-Odile Bristeau, Jacques Sainte-Marie. Derivation of a non-hydrostatic shallow water model; Comparison with Saint-Venant and Boussinesq systems. Discrete & Continuous Dynamical Systems - B, 2008, 10 (4) : 733-759. doi: 10.3934/dcdsb.2008.10.733

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