Vertically Averaged Models for the Free Surface Non-Hydrostatic Euler System: Derivation and Kinetic Interpretation

Starting from the Euler equations for incompressible flows, we propose an extension of the classical Saint-Venant system where the non-hydrostatic pressure terms are taken into account in the asymptotic expansion. We also derive a multilayer version of this vertically averaged Euler system. The multilayer approach allows mass exchanges between the neighboring layers. Finally we give a kinetic type interpretation for the proposed models.