Geophysical flows under location uncertainty, Part I Random transport and general models

Valentin Resseguier 1, 2, * Etienne Mémin 2 Bertrand Chapron 1
* Auteur correspondant
2 FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences
IRMAR - Institut de Recherche Mathématique de Rennes, IRSTEA - Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture, Inria Rennes – Bretagne Atlantique
Abstract : A stochastic flow representation is considered with the Eulerian velocity decomposed between a smooth large scale component and a rough small-scale turbulent component. The latter is specified as a random field uncorrelated in time. Subsequently, the material derivative is modified and leads to a stochastic version of the material derivative to include a drift correction , an inhomogeneous and anisotropic diffusion, and a multiplicative noise. As derived, this stochastic transport exhibits a remarkable energy conservation property for any realizations. As demonstrated, this pivotal operator further provides elegant means to derive stochastic formulations of classical representations of geophysical flow dynamics.
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Valentin Resseguier, Etienne Mémin, Bertrand Chapron. Geophysical flows under location uncertainty, Part I Random transport and general models. Geophysical and Astrophysical Fluid Dynamics, Taylor & Francis, 2017, 111 (3), pp.149-176. 〈10.1080/03091929.2017.1310210〉. 〈hal-01391420v3〉

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