Likely chaotic transitions of large-scale fluid flows using a stochastic transport model

Valentin Resseguier 1 Etienne Mémin 1 Bertrand Chapron 2
1 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 : Characterizing and tracking the chaotic transitions of a flow model is generally not an easy task. This problem is still a major issue in ensemble forecasting for climate predictions and for simulating geophysical flows. A natural way to explore likely transitions consists in randomizing the model parameters, the initial condition or the dynamics through a random forcing. Randomizing the initial conditions seems the more natural way to study chaos. However, the initial perturbations of interest mostly live at small spatial scales. Without prior, a lot of realizations are thus needed to well represent all those possible perturbations. Moreover, at the resolved scales, numerical simulations make use of diffusive operator to model the effect of unresolved velocity. Therefore, initial small-scale perturbations are often diffused before triggering any chaotic transition. Randomizing the dynamics can then more continuously introduces small-scales perturbations. Here, general randomized fluid dynamic models rely on the decomposition of the velocity between a large-scale component and a random one, Gaussian, uncorrelated in time, possibly anisotropic and inhomogeneous in space. Using the Ito-Wentzell formula, the stochastic partial differential equation of a tracer transported is derived. This equation introduces a drift correction, an inhomogeneous anisotropic diffusion and a multiplicative noise. As interpreted, the two first terms provide a theoretical justification and a generalization of many empirical deterministic subgrid tensors. This conservative model thus readily provides a clear physical link between the amount of numerical diffusion and the amount of noise. To illustrate our purpose, simulations at high-resolution of a Surface Quasi-Geostrophic model have been performed. Metastable symmetries in the initial condition break after 40 days of advection, leading to a deterministic chaotic transition. For a fixed initial condition, the deterministic simulation at a coarser resolution appears to follow a completely different transition than the high-resolution simulation, leading to large errors. Contrarily, low-resolution stochastic model simulations are found to follow and well capture both transitions with only 200 realizations.
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https://hal.inria.fr/hal-01377702
Contributeur : Valentin Resseguier <>
Soumis le : mercredi 9 novembre 2016 - 18:13:53
Dernière modification le : mercredi 11 avril 2018 - 02:00:06
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  • HAL Id : hal-01377702, version 1

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Valentin Resseguier, Etienne Mémin, Bertrand Chapron. Likely chaotic transitions of large-scale fluid flows using a stochastic transport model. 9th Chaotic Modeling and Simulation International Conference (CHAOS2016), May 2016, Londres, United Kingdom. 〈http://www.cmsim.org/chaos2016.html〉. 〈hal-01377702〉

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