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

TL;DR

This paper presents a multi-symplectic formulation of the two-layer Serre-Green-Naghdi equations, enabling the use of structure-preserving numerical schemes for large amplitude internal gravity waves.

Contribution

It introduces a multi-symplectic structure for the Serre-Green-Naghdi equations, facilitating structure-preserving numerical methods for modeling internal gravity waves.

Findings

Multi-symplectic formulation derived for two-layer internal waves.

Enables application of multi-symplectic integrators like Euler or Preissman schemes.

Preserves multi-symplecticity at the discrete level.

Abstract

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.