Skip to Main content Skip to Navigation
Journal articles

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.
Document type :
Journal articles
Complete list of metadata
Contributor : Jacques Sainte-Marie Connect in order to contact the contributor
Submitted on : Monday, August 22, 2016 - 11:12:58 AM
Last modification on : Tuesday, April 19, 2022 - 10:17:27 AM
Long-term archiving on: : Wednesday, November 23, 2016 - 11:58:38 AM


Files produced by the author(s)


  • HAL Id : hal-01011691, version 2
  • ARXIV : 1406.6565


Marie-Odile Bristeau, Anne Mangeney, Jacques Sainte-Marie, Nicolas Seguin. An energy-consistent depth-averaged Euler system: derivation and properties.. Discrete and Continuous Dynamical Systems - Series B, American Institute of Mathematical Sciences, 2015, 20 (4), pp.28. ⟨hal-01011691v2⟩



Record views


Files downloads