Shallow water asymptotic models for the propagation of internal waves

2013/06/30 by Vincent Duchêne, Vincent Duchene, Samer Israwi +1 · 16 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Calculus (dental) #Consistency (knowledge bases) #Dimension (graph theory) #Exposition (narrative) #Geology #Geometry #Internal wave #Mathematical analysis #Mathematics #Mechanics #Nonlinear Waves and Solitons #Ocean Waves and Remote Sensing #Physics #Pure mathematics #Shallow water equations #Type (biology) #Waves and shallow water #Work (physics) #math.AP

paper · pdf · doi:10.3934/dcdss.2014.7.239

published in Discrete and Continuous Dynamical Systems - S 7(2), 239-269 (American Institute of Mathematical Sciences) · Proceeding of the workshop " mécanique des fluides et dynamique de populations : modèles, existence de solutions, stabilité et méthodes numériques ", Beirut, Sept. 10-14, 2012

arxiv created 2013/07/12 · openalex publication_date 2013/09/17 · arxiv updated 2021/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

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