Experimental analysis of cumulants scaling properties in fully developed intermittent turbulence

We consider velocity structure functions in turbulence through an approach using cumulants, and for a fixed value of the distance l. This allows to consider the cumulant generating function Phi(l)(q) = log(vertical bar Delta V-l vertical bar(q)). 'Using an atmospheric turbulent database, we show that the cumulant generating function is nonanalytic, with a development compatible with a log-stable model of the form Phi(l)(q) = A(l)q + B(l)q(alpha) and a parameter value of alpha = 1.5. The parameters A(l) and B-l are experimentally estimated: they are respectively increasing and decreasing functions of (l); their scaling ranges correspond to the scaling range of the velocity fluctuations. The dependence between these two functions is studied in relation to Extended Self Similarity and Generalized Extended Self Similarity properties.