CASTRO, Angel; LANNES, David

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CASTRO, Angel
Departamento de Matematicas

LANNES, David
Institut de Mathématiques de Bordeaux [IMB]

Langue

Article de revue

Ce document a été publié dans

Journal of Fluid Mechanics. 2014, vol. 759, p. 642-675

Cambridge University Press (CUP)

Résumé en anglais

We study here Green-Naghdi type equations (also called fully nonlinear Boussinesq, or Serre equations) modeling the propagation of large amplitude waves in shallow water without smallness assumption on the amplitude of the waves. The novelty here is that we allow for a general vorticity, hereby allowing complex interactions between surface waves and currents. We show that the a priori 2+1-dimensional dynamics of the vorticity can be reduced to a finite cascade of two-dimensional equations: with a mechanism reminiscent of turbulence theory, vorticity effects contribute to the averaged momentum equation through a Reynolds-like tensor that can be determined by a cascade of equations. Closure is obtained at the precision of the model at the second order of this cascade. We also show how to reconstruct the velocity field in the 2 + 1 dimensional fluid domain from this set of 2-dimensional equations and exhibit transfer mechanisms between the horizontal and vertical components of the vorticity, thus opening perspectives for the study of rip currents for instance.< Réduire

URI

https://oskar-bordeaux.fr/handle/20.500.12278/194580

Project ANR

DYnamique des Fluides, Couches Limites, Tourbillons et Interfaces - ANR-13-BS01-0003
Frontières, numérique, dispersion. - ANR-13-BS01-0009

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Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251