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An Introduction to Large Deviations and Equilibrium Statistical Mechanics for Turbulent Flows

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Stochastic Equations for Complex Systems

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Abstract

Two-dimensional turbulent flows, and to some extent, geophysical flows, are systems with a large number of degrees of freedom, which, albeit fluctuating, exhibit some degree of organization: coherent structures emerge spontaneously at large scales. In this short course, we show how the principles of equilibrium statistical mechanics apply to this problem and predict the condensation of energy at large scales and allow for computing the resulting coherent structures. We focus on the structure of the theory using the language of large deviation theory.

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  1. National Center for Atmospheric Research, Boulder, CO, 80307, USA

    Corentin Herbert

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  1. University of Wyoming, Laramie, Wyoming, USA

    Stefan Heinz

  2. University of Wyoming, Laramie, Wyoming, USA

    Hakima Bessaih

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Herbert, C. (2015). An Introduction to Large Deviations and Equilibrium Statistical Mechanics for Turbulent Flows. In: Heinz, S., Bessaih, H. (eds) Stochastic Equations for Complex Systems. Mathematical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-18206-3_3

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  • DOI: https://doi.org/10.1007/978-3-319-18206-3_3

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