A Langevin equation for the energy cascade in fully-developed turbulence

Abstract

Experimental data from a turbulent jet flow is analysed in terms of an additive, continuous stochastic process where the usual time variable is replaced by the scale. We show that the energy transfer through scales is well described by a linear Langevin equation, and discuss the statistical properties of the corresponding random force in detail. We find that the autocorrelation function of the random force decays rapidly: the process is therefore Markov for scales larger than Kolmogorov's dissipation scale $η$. The corresponding autocorrelation scale is identified as the elementary step of the energy cascade. However, the probability distribution function of the random force is both non-Gaussian and weakly scale-dependent.