Etude mathématique de modèles de couches visqueuses pour des écoulements naturels

Abstract : Shallow Water system is widely used for flows when the depth is smaller than the longitudinal scale. The establishment needs some hypothesis on the velocity profile in order to describe the moment flux and the shear stress on ground. In this thesis, we present a two layer decomposition of the fluid between an ideal fluid and a viscous layer in the spirit of the Interactive Boundary Layer (IBL) introduced in aeronautics. This interaction leads to obtain in our equations a friction term which fits with the physical expectations for the local maximum. So a major part of this work is interested in the comprehension of the viscous layer where the velocity profile is confined. The study is based on the writing of Prandtl equations then the establishment of the von Kármán equation. The last one contains the necessary quantities for a definition of the researched flux. Also this equation is essential for a closure of the system. Some numerical results illustrate the proposed model with the association of ideal fluid ans viscous layer. A last chapter presents two alternatives formulations of the model based on an ideal fluid with modified boundary conditions. The first one keeps the same domain but has a transpiration boundary.
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Mathilde Legrand. Etude mathématique de modèles de couches visqueuses pour des écoulements naturels. Mathématiques générales [math.GM]. Université d'Orléans, 2016. Français. ⟨NNT : 2016ORLE2047⟩. ⟨tel-01529756⟩

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