Thermodynamic description of the relaxation of two-dimensional turbulence using Tsallis statistics.

Abstract

Two-dimensional Euler turbulence and drift turbulence in a pure-electron plasma column have been experimentally observed to relax to metaequilibrium states that do not maximize the Boltzmann entropy, but rather seem to minimize enstrophy. We show that a recent generalization of thermodynamics and statistics due to Tsallis [Phys. Lett. A 195, 329 (1994); J. Stat. Phys. 52, 479 (1988)] is capable of explaining this phenomenon in a natural way. In particular, the maximization of the generalized entropy ${S}_{q}$ with $q=\frac{1}{2}$ for the pure-electron plasma column leads to precisely the same profiles predicted by the restricted minimum enstrophy theory of Huang and Driscoll [Phys. Rev. Lett. 72, 2187 (1994)]. These observations make possible the construction of a comprehensive thermodynamic description of two-dimensional turbulence.