  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.
