Should we abandon cascade models to describe the spatial complexity of fully developed turbulence velocity profiles?

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We perform one- and two-points magnitude cumulant analysis of one-dimensional longitudinal velocity profiles stemming from three different experimental set-ups and covering a broad range of Taylor scaled Reynolds numbers from 89 to 2500. While the first-order cumulant behavior is found to strongly depend on Reynolds number and experimental conditions, the second-order cumulant and the magnitude connected correlation functions are shown to display respectively universal scale and space-lag behavior. Despite the fact that the Extended Self-Similarity (ESS) hypothesis is not consistent with these findings, when extrapolating our results to the limit of infinite Reynolds number, one confirms the validity of the log-normal multifractal description of the intermittency phenomenon with a well defined intermittency parameter C2 = 0.025 +/- 0.003. But the convergence to zero of the magnitude connected correlation functions casts doubt on the asymptotic existence of an underlying multiplicative cascading spatial structure.