Non-extensive statistical mechanics approach to fully developed hydrodynamic turbulence

We apply non-extensive methods to the statistical analysis of fully developed turbulent flows. Probability density functions of velocity differences at distance r obtained by extremizing the Tsallis entropies coincide well with what is measured in turbulence experiments, The coincidence is much better than that of e.g. Levy distributions. We derive a set of relations between the hyperflatness factors F,, and the non-extensitivity parameter q, which can be used to directly extract the function q(r) from experimentally measured structure functions. We comment on various non-extensive methods to calculate the moment scaling exponents zeta (m). (C) 2001 Elsevier Science Ltd. All rights reserved.