Tsallis statistics and turbulence

In order to reveal the underlying statistics describing properly the fully developed turbulence, the probability density function of the local dissipa tion is derived by taking extremal of a generalized entropy (Tsallis entrop y) under the two constraints, i.e., one is the normalization of probability and the other is to fix the intermittency exponent being constant. The gen eralized entropy includes the Boltzmann-Gibbs entropy as a special case whe re the Tsallis index q is equal to 1. The multifractal spectrum f (alpha) c orresponding to the probability density function is determined self-consist ently in the sense that all quantities can be determined by the observed va lue of the intermittency exponent. It is shown that the scaling exponents z eta (m) of velocity structure function derived by making use of f(alpha) ex plains experimental data very well. It is also revealed that the asymptotic expression of zeta (m) for m much greater than I has a log term. The Tsall is index q turns out to be 0.380 which manifests itself that the system of fully developed turbulence has a nonextensive character. (C) 2001 Elsevier Science Ltd. All rights reserved.