A note on three-point statistics of velocity increments in turbulence

We consider the joint probability functions f(v(3), L-3; v(2), L-2; v(1), L-1) for the velocity increments v(L) across scale L of a turbulent field measured in the helium gas jet experiment of Chabaud et al. (Chabaud B. et al., Phys. Rev. Lett., 73 (1994) 3227). We show that the conditional probability distribution p(v(3), L-3/v(2),L-2; v(1), L-1), L-1 > L-2 > L-3, becomes independent of v(1) and L-1 provided L-1 - L-2 > L-mar, where L-mar is comparable to the crossover scale from the inertial to the viscous subrange. This indicates that the N-point probability distributions f(v(N), L-N;...v(2), L-2; v(1), L-1) may be considered as a stochastic process exhibiting Markovian properties.