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1 LAMA - Laboratoire de Mathématiques 2 JAD - Laboratoire Jean Alexandre Dieudonné 3 LOCIE - Laboratoire Optimisation de la Conception et Ingénierie de l-Environnement

Abstract : This manuscript is devoted to the modelling of water waves in the deep water regime with some emphasis on the underlying variational structures.
The present article should be considered as a review of some existing models and modelling approaches even if new results are presented as well.
Namely, we derive the deep water analogue of the celebrated Serre-Green-Naghdi equations which have become the standard model in shallow water environments.
The relation to existing models is discussed.
Moreover, the multi-symplectic structure of these equations is reported as well.
The results of this work can be used to develop various types of robust structure-preserving variational integrators in deep water.
The methodology of constructing approximate models presented in this study can be naturally extrapolated to other physical flow regimes as well.

Keywords : Serre-Green-Naghdi equations deep water approximation free surface impermeability variational principle

Autor: Denys Dutykh - Didier Clamond - Marx Chhay -



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