2005: Relative dispersion in 2D stochastic flows

We investigate the relative dispersion for two types of stochastic flows—Brownian flow (Kraichnan model) and a flow with memory (inertial particles). In the first case well-known asymptotics are rigorously derived for a self-similar spectrum of the velocity field by using a half-century-old Feller’s theorem. Exact limits of the asymptotics and exact values for dimensionless constants are obtained. The second part of the paper addresses a relatively new object: the first-order Markov stochastic flow modelling inertial particle motion. Both local and non-local dynamics are investigated. In the first case an exact exponential asymptotic is obtained for the relative dispersion. In turn, two regimes are considered in the case of non-smooth forcing: weak and strong turbulence. For weak turbulence the obtained asymptotic of relative dispersion is similar to that of the Brownian flow. As for strong turbulence, an upper bound is obtained for the scaling of relative dispersion