Article Dans Une Revue Studies in Applied Mathematics Année : 2016

A new class of two-layer Green-Naghdi systems with improved frequency dispersion

Résumé

We introduce a new class of Green-Naghdi type models for the propagation of internal waves between two (1+1)-dimensional layers of homogeneous, immiscible, ideal, incompressible, irrotational fluids, vertically delimited by a flat bottom and a rigid lid. These models are tailored to improve the frequency dispersion of the original bi-layer Green-Naghdi model, and in particular to manage high-frequency Kelvin-Helmholtz instabilities, while maintaining its precision in the sense of consistency. Our models preserve the Hamiltonian structure, symmetry groups and conserved quantities of the original model. We provide a rigorous justification of a class of our models thanks to consistency, well-posedness and stability results. These results apply in particular to the original Green-Naghdi model as well as to the Saint-Venant (hydrostatic shallow-water) system with surface tension.

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Dates et versions

hal-01127972 , version 1 (09-03-2015)
hal-01127972 , version 2 (10-02-2016)

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Vincent Duchêne, Samer Israwi, Raafat Talhouk. A new class of two-layer Green-Naghdi systems with improved frequency dispersion. Studies in Applied Mathematics, 2016, 137 (3), pp.356-415. ⟨10.1111/sapm.12125⟩. ⟨hal-01127972v2⟩
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