TOWARDS LOG-NORMAL STATISTICS IN HIGH REYNOLDS-NUMBER TURBULENCE

We report on the experimental application of a wavelet based deconvolu tion method that has been recently emphasized as a very efficient tool to extract some underlying multiplicative cascade process from synthe tic turbulent signals. For high Reynolds number wind tunnel turbulence (R(lambda)similar or equal to 2000), using large velocity records (ab out 25 x 10(3) integral time scales), a cascading process is identifie d and found to be log-normal. This result relies on the Gaussian shape of the kernel G(aa'), that determines the nature of the cascade from a scale a' to a finer scale a. It is confirmed by investigating variou s standard quantities such as the probability density functions of the wavelet transform coefficients or the scaling exponents zeta(q) that characterize the evolution across the scales of the moments of these d istributions. Log-normal statistics are shown to hold on a well define d range of scales; that can be further used as an objective definition of the inertial range, and to depend on the Reynolds number. We comme nt on the asymptotic validity of the log-normal multifractal descripti on.