Multi-symplectic structure of fully-nonlinear weakly-dispersive internal gravity waves

Didier Clamond (1) , Denys Dutykh (2, 3, 4)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 LAMA - Laboratoire de Mathématiques
3 INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques
4 USMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont Blanc

In this short communication we present the multi-symplectic structure for the two-layer Serre-Green-Naghdi equations describing the evolution of large amplitude internal gravity long waves. We consider only a two-layer stratification with rigid bottom and lid for simplicity, generalisations to several layers being straightforward. This multi-symplectic formulation allows the application of various multi-symplectic integrators (such as Euler or Preissman box schemes) that preserve exactly the multi-symplecticity at the discrete level.

Mots clés: multi-symplectic structure; Green-Naghdi equations; long waves; internal waves; two-layer flow

Domaines: Mécanique des fluides [physics.class-ph]; Equations aux dérivées partielles [math.AP]; Analyse classique [math.CA]; Formation de Structures et Solitons [nlin.PS]; Systèmes Solubles et Intégrables [nlin.SI]; Physique mathématique [math-ph]; Physique Atmosphérique et Océanique [physics.ao-ph]; Dynamique des Fluides [physics.flu-dyn]

Didier Clamond, Denys Dutykh. Multi-symplectic structure of fully-nonlinear weakly-dispersive internal gravity waves. Journal of Physics A: Mathematical and Theoretical, 2016, 49, pp.31LT01. ⟨10.1088/1751-8113/49/31/31LT01⟩. ⟨hal-01296552v2⟩