Complete multiplier statistics explained by stochastic cascade processes

Abstract

Abstract The prevalent understanding of fully developed turbulence is that of a cascade in which vortices successively break up into smaller ones. Based on this idea, theoretical developments were often concerned with multiplicative random cascade processes. We focus on the velocity fluctuations and derive a closed as well as complete statistical description of the underlying velocity multipliers using a Fokker–Planck equation, which is estimated directly from experimental data. This shed new light on the statistics of multipliers and their often assumed independence. For the heavy-tailed statistical features of the multipliers, close to a Cauchy distribution, no intermittency of turbulence is needed.