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Derivation of viscous Saint-Venant system for laminar shallow water; Numerical validation
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.