Two-Particle Dispersion in Model Velocity Fields

Abstract

We consider two-particle dispersion in a velocity field, where the relative two-point velocity scales according to $v^{2}(r)\propto r^α$ and the corresponding correlation time scales as $τ(r)\propto r^β$, and fix $α=2/3$, as typical for turbulent flows. We show that two generic types of dispersion behavior arize: For $α/2+β< 1$ the correlations in relative velocities decouple and the diffusion approximation holds. In the opposite case, $α/2+β>1$, the relative motion is strongly correlated. The case of Kolmogorov flows corresponds to a marginal, nongeneric situation.