Revealing a lognormal cascading process in turbulent velocity statistics with wavelet analysis

We use the continuous wavelet transform to extract a cascading process from experimental turbulent velocity signals. We mainly investigate various statistical quantities such as the singularity spectrum, the self-similarity kernel and space-scale correlation functions, which together provide information about the possible existence and nature of the underlying multiplicative structure. We show that, at the highest accessible Reynolds numbers, the experimental data do not allow us to distinguish various phenomenological cascade models recently proposed to account for intermittency from their lognormal approximation. In addition, we report evidence that velocity fluctuations are not scale-invariant but possess more complex self-similarity properties, which are likely to depend on the Reynolds number. We comment on the possible asymptotic validity of the multifractal description.