Algorithmes de Schwarz et couplage océan-atmosphère

Florian Lemarié 1
1 MOISE - Modelling, Observations, Identification for Environmental Sciences
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : Many applications in coastal and operational oceanography and meteorology require high resolution local models, for which ocean-atmosphere interactions must be properly taken into account. In that case, connecting the two model solutions at the air-sea interface is a very difficult problem. In this context we intend to adapt Schwarz-like domain decomposition methods to this kind of problem to address it on an appropriate way from the mathematical point of view. One important difficulty comes from the turbulent behaviour of the flow in the boundary layers both sides of the interface. First, we carry out a review of the various parameterization schemes relevant for our study. Then we propose to study an idealized form of the problem: a coupling between two diffusion equations modeling the turbulent mixing in the boundary layers, the diffusion coefficients are given by usual parameterization schemes. In order to ensure a quick convergence of the method we search for optimized transmission conditions. Those latter are determined analytically for constant and discontinuous at the interface diffusion coefficients then we extend those results to the more complicated case with spatially variable coefficients, thanks to a new approach. Finally we show how the usual coupling methods can be described in the formalism of the Schwarz methods. Then we propose a first real-case study (genesis and propagation of a tropical cyclone) and we introduce some numerical results, obtained with a non-optimized method.
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Florian Lemarié. Algorithmes de Schwarz et couplage océan-atmosphère. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2008. Français. ⟨tel-00343501⟩

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