Analysis of turbulence by statistics based on generalized entropies

An analytical formula of the scaling exponents of velocity structure functi on for fully developed turbulence is derived, non-perturbatively, by assumi ng that its underlying statistics is the one based on the generalized measu res of entropy, the Renyi entropy or the Havrda-Charvat-Tsallis (HCT) entro py. It is revealed by a self-consistent analysis for the observed value mu = 0.220 (+/-1%) that the formula explains experimental data very well with single value, q = 0.343, of the index which appears in the measures of the Renyi entropy or of the HCT entropy. The probability density functions of t he velocity fluctuation and of the velocity gradient are also presented. (C ) 2001 Elsevier Science B.V. All rights reserved.