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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

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 and Continuous Dynamical Systems - B, 2008, 10 (4) : 733-759. doi: 10.3934/dcdsb.2008.10.733
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