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Derivation of Maximum Entropy Principles in Two-Dimensional Turbulence via Large Deviations

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Abstract

The continuum limit of lattice models arising in two-dimensional turbulence is analyzed by means of the theory of large deviations. In particular, the Miller–Robert continuum model of equilibrium states in an ideal fluid and a modification of that model due to Turkington are examined in a unified framework, and the maximum entropy principles that govern these models are rigorously derived by a new method. In this method, a doubly indexed, measure-valued random process is introduced to represent the coarse-grained vorticity field. The natural large deviation principle for this process is established and is then used to derive the equilibrium conditions satisfied by the most probable macrostates in the continuum models. The physical implications of these results are discussed, and some modeling issues of importance to the theory of long-lived, large-scale coherent vortices in turbulent flows are clarified.

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Authors and Affiliations

  1. Department of Mathematics, Illinois Wesleyan University, Bloomington, Illinois, 61702

    Christopher Boucher

  2. Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts, 01003

    Richard S. Ellis

  3. Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts, 01003

    Bruce Turkington

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  1. Christopher Boucher
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  2. Richard S. Ellis
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  3. Bruce Turkington
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Boucher, C., Ellis, R.S. & Turkington, B. Derivation of Maximum Entropy Principles in Two-Dimensional Turbulence via Large Deviations. Journal of Statistical Physics 98, 1235–1278 (2000). https://doi.org/10.1023/A:1018671813486

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