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arXiv · 1406.6565

An energy-consistent depth-averaged Euler system: derivation and properties

Marie-Odile Bristeau·Anne Mangeney·Jacques Sainte-Marie·Nicolas Seguin
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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.

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Marie-Odile Bristeau, Anne Mangeney, Jacques Sainte-Marie, Nicolas Seguin. 2014-06-25. An energy-consistent depth-averaged Euler system: derivation and properties. https://arxiv.org/abs/1406.6565

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