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

Didier Clamond (1) , Denys Dutykh (2)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 LAMA - Laboratoire de Mathématiques

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

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. 2016. ⟨hal-01296552v1⟩