Abstract
In order to reveal the underlying statistics describing properly the fully developed turbulence, the probability density function of the local dissipation is derived by taking extremal of a generalized entropy (Tsallis entropy). It is shown that the scaling exponent ζm of velocity structure function, determined non-perturbatively with the help of the derived probability density function, explains experimental data very well. It is also revealed that the asymptotic expression of ζm for m >> 1. has a log term. The present analysis strongly suggests that the underlying statistics of fully developed turbulence is the non-extensive one.
