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 aminimal energy constraint instead of an asymptotic expansion. The model slightly differs from thewell-known Green-Naghdi model and is confronted with stationary andanalytical solutions of the Euler system corresponding to rotationalflows. At the end of the paper, we givetime-dependent analytical solutions for the Euler system that are alsoanalytical solutions for the proposed model but that are not solutionsof the Green-Naghdi model. We also give and compare analytical solutions of thetwo non-hydrostatic shallow water models.
Cite
@article{arxiv.1406.6565,
title = {An energy-consistent depth-averaged Euler system: derivation and properties},
author = {Marie-Odile Bristeau and Anne Mangeney and Jacques Sainte-Marie and Nicolas Seguin},
journal= {arXiv preprint arXiv:1406.6565},
year = {2016}
}