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From the free surface Navier-Stokes system, we derive the non-hydrostaticSaint-Venant system for the shallow waters including friction and viscosity.The derivation leads to two formulations of growing complexity depending on thelevel of approximation chosen for the fluid pressure. The obtained models arecompared with the Boussinesq models.

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