Different methods to estimate the Einstein-Markov coherence length in turbulence.

We study the Markov property of experimental velocity data of different homogeneous isotropic turbulent flows. In particular, we examine the stochastic "cascade" process of nested velocity increments ξ(r):=u(x+r)-u(x) as a function of scale r for different nesting structures. It was found in previous work that, for a certain nesting structure, the stochastic process of ξ(r) has the Markov property for step sizes larger than the so-called Einstein-Markov coherence length l(EM), which is of the order of magnitude of the Taylor microscale λ [Phys.

Defining a new class of turbulent flows.

We apply a method based on the theory of Markov processes to fractal-generated turbulence and obtain joint probabilities of velocity increments at several scales. From experimental data we extract a Fokker-Planck equation which describes the interscale dynamics of the turbulence. In stark contrast to all documented boundary-free turbulent flows, the multiscale statistics of velocity increments, the coefficients of the Fokker-Planck equation, and dissipation-range intermittency are all independent of Rλ (the characteristic ratio of inertial to viscous forces in the fluid).