Experimental Analysis of Self-Similarity and Random Cascade Processes: Application to Fully Developed Turbulence Data

In the context of fully developed turbulence, Castaing et al. [10] have recently advocated a description of a random cascade process in terms of a kernel $G_{aa'} (x)$ that characterizes the nature of the cascade when going from a scale $a'$ to a finer scale $a$. We elaborate on a method to estimating, directly from experimental data, the shape of $G_{aa'}$ for all scales $a$ and $a'$. We apply this method to turbulent velocity data and we show that it provides very instructive informations about the soundness of various phenomenological models for the intermittency character of turbulent flows