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

(Received 4 November 1996, received in final form 19 December 1996, accepted 19 December 1996)

Abstract
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.