Derivation of viscous Saint-Venant system for laminar shallow water; Numerical validation
Jean-Frédéric Gerbeau - INRIA- Project M3N, Rocquencort B.P. 105, F-78153 Le Chesnay Cedex, France (email)
Abstract: We derive the Saint-Venant system for the shallow waters including small friction, viscosity and Coriolis-Boussinesq factor departing from the Navier-Stokes system with a free moving boundary. This derivation relies on the hydrostatic approximation where we follow the role of viscosity and friction on the bottom. Numerical comparisons between the limiting Saint-Venant system and direct Navier-Stokes simulation allow to validate this derivation.
Keywords: Navier-Stokes equations, Saint-Venant equations, shallow water, free
surface, asymptotic analysis, viscosity, friction.
Received: November 2000; Revised: January 2001; Available Online: January 2001.
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