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A shallow water model with eddy viscosity for basins with varying bottom topography
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In this article, the authors introduce appropriate scalings into a three-dimensional anisotropic eddy viscosity model to derive a two-dimensional shallow water model and prove the global regularity of the resulting model.Abstract:
The motion of an incompressible fluid confined to a shallow basin with a varying bottom topography is considered. We introduce appropriate scalings into a three-dimensional anisotropic eddy viscosity model to derive a two-dimensional shallow water model. The global regularity of the resulting model is proved. The anisotropic form of the stress tensor in our three-dimensional eddy viscosity model plays a critical role in ensuring that the resulting shallow water model dissipates energy.read more
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Effet cosinus sur un modèle visqueux de type Saint-Venant et ses équations limites de type quasi-géostrophique et lacs
TL;DR: In this article, a methodologie certes classique dans le domaine de l'analyse asymptotique (developpement en serie), nous montrerons que de nouveaux termes dependant du cosinus de la latitude ont ete oublies dans des papiers recents and doivent etre pris en compte pour certaines applications en geophysique.
Dissertation
Effets de petites échelles, du tenseur des contraintes, des conditions au fond et à la surface sur les équations de Saint-Venant
TL;DR: In this paper, the authors present a new model for sedimentation of visco-plastiques based on the equations of Saint-Venant, a modele with an "effet cosinus", which permet de bien capter la couche limite mais aussi d'ajouter le terme de topographie.
Dissertation
Sur quelques modèles hétérogènes en mécanique des fluides
TL;DR: In this paper, the authors present a model of a fluide visqueux newtonien and incompressible with respect to a sinky bathymetrie, which degenere proche du bord.
Journal ArticleDOI
Long time behavior for a dissipative shallow water model
TL;DR: In this article, the authors consider the two-dimensional shallow water model and construct the approximate inertial manifolds for the associated dynamical system and estimate its order, and prove the L 2 asymptotic decay of the weak solutions.
A two-dimensional method for a dispersive shallow water model
Nora Aïssiouene,Marie-Odile Bristeau,Edwige Godlewski,Anne Mangeney,Carlos Parés,Jacques Sainte-Marie +5 more
TL;DR: In this paper, a numerical method for a two-dimensional dispersive shallow water system with topography is proposed, which is a depth averaged Euler system and takes into account a non-hydrostatic pressure which implies to solve an incompressible system.
References
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Book
An Introduction to Fluid Dynamics
TL;DR: The dynamique des : fluides Reference Record created on 2005-11-18 is updated on 2016-08-08 and shows improvements in the quality of the data over the past decade.
Book
Navier-Stokes Equations: Theory and Numerical Analysis
TL;DR: This paper presents thediscretization of the Navier-Stokes Equations: General Stability and Convergence Theorems, and describes the development of the Curl Operator and its application to the Steady-State Naviers' Equations.
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