Séminaire EDPAN

Décembre 2024

• Jeudi 12 décembre 2024 - Thomas Alazard

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• Jeudi 05 décembre 2024 - Nathanaël Boutillon

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Novembre 2024

• Jeudi 21 novembre 2024 - Jérôme Coville

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• Jeudi 14 novembre 2024 - Lorenzo Brandolese

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Octobre 2024

• Jeudi 17 octobre 2024 - Frédéric Charve

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Septembre 2024

• Jeudi 26 septembre 2024 - Sophie Thery

  Well-posedness of a non-local ocean-atmosphere coupling model

  Ocean-atmosphere interactions play a critical role in climate modeling and weather forecasting. Ocean and atmosphere models have been constructed separately by two distinct communities and coupled via complex interface conditions. We propose a translation of this coupled system into a global mathematical model in order to use the tools of analysis and study its well-posedness. We present a simplified but realistic model containing the main ingredients of numerical models. This mathematical model is known as the coupled Ekman problem, considering vertical exchanges of the horizontal currents, the Coriolis effect, and the effect of small scales via turbulent viscosities. The particularity of this model is to consider the interface as a buffer zone between the two domains with interface conditions specific to the ocean-atmosphere coupling. These interface conditions lead to the dependence of viscosity profiles on the jumps of the current around the interface and make the global problem non-local. To study the well-posedness of this system, a first method is rewrite it as a fixed point problem in order to deal with the non-local aspects. A general study of the problem in its stationary and non-stationary state leads to a sufficient condition to guarantee the well-posedness that depend on the variation of the viscosity profile. This condition applied to the ocean-atmosphere framework, i.e. with physically-realistic viscosity profiles and orders of magnitude, is too restrictive and does not guarantee the uniqueness of solutions. In the stationary case, a necessary and sufficient condition can be given to ensure the existence and uniqueness of solutions. We will see that, once again, in the context of ocean-atmosphere coupling, this condition is not met and there is no uniqueness of solutions. In conclusion, we will discuss the prospects for such a model and the parameters that could be adjusted to obtain a mathematically well-posed model.

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