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Etude numérique des algorithmes de couplage océan-atmosphère avec prise en compte des paramétrisations physiques des couches limites

Sophie Thery 1, 2 
2 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows
Inria Grenoble - Rhône-Alpes, UGA - Université Grenoble Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : Ocean-atmosphere interactions play a major role in many geophysical phenomena such as tropical cyclones or climate change. Recent studies show that the current methods for carrying out this coupling in numerical models are mathematically unsatisfactory. As an alternative to better represent the interaction between these two media, we propose in this thesis to apply an iterative process, more precisely the Schwarz algorithms resulting from the domain decomposition methods. In our context, the systems involved are very complex and require simplifications to be analyzed analytically. These simplifications lead us to consider a 1D vertical coupling of two diffusion-type equations. The parametrization of turbulent phenomena in the ocean and the atmosphere, and particularly at their interface, reveals peculiarities specific to this application. A first feature is to consider viscosity coefficients that are not constant in space, and discontinuous at the interface. A second feature is to consider the Earth's rotation, via the Coriolis effect. Finally, a third characteristic of our model is that the exchanges at the interface are treated in a complex way and create non-linearities in the coupled model via the interface conditions.We study this problem, and the role of the different specificities on the behavior of the algorithm, with various degrees of complexity, first in the framework of the coupled Ekman problem (linear problem) then in the non-linear framework. In particular, it has been shown that the different specificities inherent in this coupling problem, never taken into account in previous theoretical studies, have a non-negligible influence on the convergence properties.
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Submitted on : Friday, June 11, 2021 - 1:51:08 PM
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Sophie Thery. Etude numérique des algorithmes de couplage océan-atmosphère avec prise en compte des paramétrisations physiques des couches limites. Analyse numérique [cs.NA]. Université Grenoble Alpes [2020-..], 2021. Français. ⟨NNT : 2021GRALM003⟩. ⟨tel-03258179v3⟩

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