AN ENERGY-CONSISTENT DEPTH-AVERAGED EULER SYSTEM: DERIVATION AND PROPERTIES.

In this paper, we present an original derivation process of a non- hydrostatic shallow water-type model which aims at approximating the in- compressible Euler and Navier-Stokes systems with free surface. The closure relations are obtained by a minimal energy constraint instead of an asymptotic expansion. The model slightly differs from the well-known Green-Naghdi model and is confronted with stationary and analytical solutions of the Euler system corresponding to rotational ows. At the end of the paper, we give time-dependent analytical solutions for the Euler system that are also analytical solutions for the proposed model but that are not solutions of the Green-Naghdi model. We also give and compare analytical solutions of the two non-hydrostatic shallow water models. [ABSTRACT FROM AUTHOR]