Stochastic Analysis of Turbulence n-Scale Correlations in Regular and Fractal-Generated Turbulence

Abstract

We present a stochastic analysis of turbulence data, which provides access to the joint probability of finding velocity increments at several scales. The underlying stochastic process in form of a Fokker-Planck equation can be reconstructed from given data. Intermittency effects are included. The stochastic process is Markovian for scale separations larger than the Einstein-Markov coherence length l _EM , which is closely related to the Taylor microscale λ. We extend our analysis to turbulence generated by a fractal square grid. We find that in contrast to other types of turbulence, like free-jet turbulence, the n-scale statistics of the velocity increments and the leading coefficients of the Fokker-Planck equation do not depend strongly on the Reynolds number.