Tsallis statistics and fully developed turbulence

Abstract

An analysis of fully developed turbulence is developed based on the assumption that the underlying statistics of the system is that of the Tsallis ensemble. The multifractal spectrum fT(α) corresponding to the Tsallis-type distribution function is determined self-consistently in the sense that all parameters can be obtained through the observed value of the intermittency exponent. It is shown that the scaling exponents ζm of the velocity structure function derived with the help of the multifractal spectrum fit very well with experimental data. It is revealed that the asymptotic expression of ζm for m>>1 has a log term. The present self-consistent approach narrowed down the value of intermittency exponent µ for the fully developed turbulence to µ = 0.235±0.015.