Derivation of a non-hydrostatic shallow water model; Comparison with   Saint-Venant and Boussinesq systems
  From the free surface Navier-Stokes system, we derive the non-hydrostatic Saint-Venant system for the shallow waters including friction and viscosity. The derivation leads to two formulations of growing complexity depending on the level of approximation chosen for the fluid pressure. The obtained models are compared with the Boussinesq models. 
Jacques Sainte-Marie (INRIA Rocquencourt), Marie-Odile Bristeau (INRIA   Rocquencourt)