Stochastic representation of fluid flow dynamics

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Résumé : In this talk I will describe a formalism to derive in a systematic way a large-scale stochastic representation of fluid flows dynamics that enables to take into account the inherent uncertainty attached to the flow evolution. The uncertainty introduced here is described through a random field, and aims at representing principally the small-scale effects that are neglected in the large-scale evolution model. The resulting large-scale dynamic system is obtained from a stochastic representation of the Reynolds transport theorem. This formalism enables, in the very same way as in the deterministic case, a physically relevant derivation (i.e. from the usual conservation law) of the sought evolution laws. We will review and discuss such a representation for some classical geophysical models. We will provide also several examples on its use in different contexts.