Particle dispersion in a multidimensional random flow with arbitrary temporal correlations

We study the statistics of relative distances R(t) between fluid particles in a spatially smooth random flow with arbitrary temporal correlations. Using the space dimensionality d as a large parameter we develop an effective description of Lagrangian dispersion. We describe the exponential growth of relative distances [R-2(t)] proportional to exp<2(lambda)over bar t> at different values of the ratio between the correlation and turnover rimes. We find the stretching correlation time which determines the dependence of [R1R2] on the difference t(1)-t(2). The calculation of the nest cumulant of R-2 shows that statistics of R-2 is nearly Gaussian at small times (as long as d much greater than 1) and becomes log-normal at large times when large-d approach fails for high-order moments. The crossover time between the regimes is the stretching correlation time which surprisingly appears to depend on the details of the velocity statistics at t much less than tau. We establish the dispersion of the In(R-2) in the log-normal statistics. (C) 1998 Elsevier Science B.V. All rights reserved.