On an improved model for long internal gravity waves

Didier Clamond
Université Côte d'Azur, LJAD, Parc Valrose, 06108 Nice cedex 2
We consider 2D irrotational flows of incompressible fluids stratified in two homogeneous shallow layers, bounded below by a horizontal impermeable bottom and above by a rigid lid. Weakly dispersive fully nonlinear equations of Serre-Green-Nagdhi type are often used to model long internal waves. We show how to improve these equations with better dispersive properties and reduced Kelvin-Helmholtz instability, while remaining asymptotically consistent and keeping all the conservation laws.