Towards log-normal statistics in high Reynolds number turbulence

Abstract

We report on the experimental application of a wavelet based deconvolution method that has been recently emphasized as a very efficient tool to extract some underlying multiplicative cascade process from synthetic turbulent signals. For high Reynolds number wind tunnel turbulence (Rλ≃ 2000), using large velocity records (about 25 × 103 integral time scales), a cascading process is identified and found to be log-normal. This results 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 various standard quantities such as the probability density functions of the wavelet transform coefficients or the scaling exponents ς q that characterize the evolution across the scales of the moments of these distributions. Log-normal statistics are shown to hold on a well defined range of scales, that can be further used as an objective definition of the inertial range, and to depend on the Reynolds number. We comment on the asymptotic validity of the log-normal multifractal description.