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.