Fluctuations and large deviations of Reynolds' stresses in zonal jet dynamics
L from Ricatti Gaussian
Résumé
The Reynolds stress (average of momentum fluxes) is a key quantity for the understanding of the average of a turbulent flow. In this paper we argue that both typical and rare fluctuations of the time averaged momentum flux are also very important in order to understand the slow flow evolution, from a fluid mechanics point of view. Those fluctuations are characterized by a large deviation rate function, that can be computed either empirically or theoretically. We prove that, whenever a quasilinear approximation is relevant, this large deviation rate function can be computed by solving a matrix Riccati equation. Using this observation, we compute for the first time the large deviation rate function for the Reynolds stress of a turbulent flow. We discuss the properties of both Gaussian and non Gaussian fluctuations. The study is performed for a barotropic flow on the sphere, close to a zonal jet. This work opens perspectives for the study of rare transitions between attractors in turbulent flows.
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