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

Marie-Odile Bristeau; Jacques Sainte-Marie

doi:10.3934/dcdsb.2008.10.733

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2008, Volume 10, Issue 4: 733-759. Doi: 10.3934/dcdsb.2008.10.733

This issue Previous Article Next Article Invariant measures and Statistical solutions of the globally modified Navier-Stokes equations

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

Received: March 31, 2007

Revised: May 31, 2008

Published: August 2008

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Abstract

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.

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Mathematics Subject Classification: Primary: 35Q30, 35Q35; Secondary: 76D05.

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