An energy-consistent depth-averaged Euler system: derivation and properties
Year: 2014
Type: article
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.
Institutions: ANGE: Analyse Numérique, Géophysique et Environnement, Institut de physique du globe de Paris, Laboratoire Jacques-Louis Lions, Centre d'Études et d'Expertise sur les Risques, l'Environnement, la Mobilité et l'Aménagement, University of Pittsburgh Medical Center, Université Pierre-et-Marie-Curie
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4299412003