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Chapitre D'ouvrage Année : 2005

Entropy production in turbulent mixing

Résumé

We review the statement and application of a Maximum Entropy Production (MEP) principle for the modeling of turbulence. More specifically it applies to two-dimensional turbulence, for which a formalism of statistical mechanics has been proposed. In that case entropy measures the randomness of turbulent fluctuations rather than the molecular fluctuations considered in usual thermodynamics. Nevertheless the same MEP formulation also applies in usual thermodynamics, and we first show how it provides a general understanding of the classical diffusion law. In all cases the outcome of this MEP is a form of diffusion law, with additional terms taking into account long-range interactions (it provides generalized Fokker-Planck equations). This outcome is not unique, but depends on the assumed constraints. We show how the turbulence model can be improved by taking into account all the conservation laws, and by sorting out the deterministic effects of small eddies, limiting MEP to the unknown, random contribution. Finally the extension to other systems with long-range interactions is briefly discussed. This includes applications to gravitational systems. Remarkably, the same transport equations apply in biology, to the chemotactic aggregation of bacterial population.

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hal-00261125 , version 1 (06-03-2008)

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Joël Sommeria. Entropy production in turbulent mixing. Kleidon A.; Lorenz R.D. Non-Equilibrium Thermodynamics and the production of Entropy: life, Earth, and Beyond, Springer, pp.79-91, 2005, 9783540224952. ⟨10.1007/11672906_7⟩. ⟨hal-00261125⟩

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