Two-particle dispersion in model two-dimensional velocity fields

We consider two-particle dispersion in a velocity field, where the relative two-point velocity, scales according to upsilon (2)(r) proportional to r(a lpha) and the corresponding correlation time scales as tau (r) proportional to r(beta), and fix alpha = 2/3, as typical for turbulent flows. We show t hat two generic types of dispersion behavior arize: For alpha /2 + beta < 1 the correlations in relative velocities decouple and the diffusion approxi mation holds. In the opposite case. alpha /2 + beta > 1, the relative motio n is strongly correlated. The case of Kolmogorov flows corresponds to a mar ginal, nongeneric situation. In this case, depending on the particular para meters of the flow. the dispersion behavior call be rather diffusive or rat her ballistic.