Shallow water asymptotic models for the propagation of internal waves

Abstract

We are interested in asymptotic models for the propagation of internal waves at the interface between two shallow layers of immiscible fluid, under the rigid-lid assumption. We review and complete existing works in the literature, in order to offer a unified and comprehensive exposition. Anterior models such as the shallow water and Boussinesq systems, as well as unidirectional models of Camassa-Holm type, are shown to descend from a broad Green-Naghdi model, that we introduce and justify in the sense of consistency. Contrarily to earlier works, our Green-Naghdi model allows a non-flat topography, and horizontal dimension d = 2. Its derivation follows directly from classical results concerning the one-layer case, and we believe such strategy may be used to construct interesting models in different regimes than the shallow-water/shallow-water studied in the present work.

Proceeding of the workshop " mécanique des fluides et dynamique de populations : modèles, existence de solutions, stabilité et méthodes numériques ", Beirut, Sept. 10-14, 2012

References in corpus (4)

• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• Influence of Bottom Topography on Long Water Waves
• Decoupled and unidirectional asymptotic models for the propagation of internal waves
• On the Korteweg-de Vries approximation for uneven bottoms

Cited by in corpus (4)

• A new class of two-layer Green-Naghdi systems with improved frequency dispersion
• A new fully justified asymptotic model for the propagation of internal waves in the Camassa-Holm regime
• Hydrodynamic models and confinement effects by horizontal boundaries
• Medium amplitude model for internal waves over large topography variation