Two-particle dispersion by correlated random velocity fields.

We consider the two-particle dispersion in a velocity field, where the relative two-point velocity scales according to v(2)(r) proportional, variantr(alpha) and the corresponding correlation time scales as tau(r) proportional r(beta). We show that for alpha/2+beta<1 the diffusion approximation holds, and the increase in the interparticle distances is governed by the distance-dependent diffusion coefficient K(r) proportional r(alpha+beta). The possible regimes outside of the validity of diffusion approximation are discussed. The Kolmogorov scaling in turbulent flow alpha=beta=2/3 corresponds to a borderline situation. The experimental data for this case suggest that the separation regime is probably ballistic.