Analysis of fully developed turbulence in terms of Tsallis statistics | Zendy

Toshihico Arimitsu | Zendy; Naoko Arimitsu | Zendy

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Analysis of fully developed turbulence in terms of Tsallis statistics

Author(s) -

Toshihico Arimitsu,

Naoko Arimitsu

Publication year - 2000

Publication title -

physical review. e, statistical physics, plasmas, fluids, and related interdisciplinary topics

Language(s) - English

Resource type - Journals

eISSN - 1095-3787

pISSN - 1063-651X

DOI - 10.1103/physreve.61.3237

Subject(s) - intermittency , tsallis statistics , tsallis entropy , statistical physics , physics , turbulence , observable , probability density function , exponent , multiplicative function , distribution (mathematics) , probability distribution , statistics , mathematics , quantum mechanics , mathematical analysis , thermodynamics , linguistics , philosophy

The analysis of the fully developed turbulence with the help of the binomial multiplicative process is reinvestigated from the standpoint of Tsallis nonextensive statistics in order to provide some insight in understanding the underlying physical meaning of the Tsallis ensemble. The formula is derived which relates Tsallis index q with the intermittency exponent μ that is a manifestation of multifractality of the sizes of eddies. It is shown that the probability density function of the local dissipation of turbulent kinetic energy can be represented by a distribution function of the type in Tsallis statistics with the index q determined by the experimentally observable quantity μ through the derived formula

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