An energy-consistent depth-averaged Euler system: derivation and properties.
Abstract
In this paper, we present an original derivation process of a
non-hydrostatic shallow water-type model which aims at approximating
the incompressible 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
flows. 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.
Origin : Files produced by the author(s)