Universal long-time properties of Lagrangian statistics in the Batchelor regime and their application to the passive scalar problem

We consider the transport of dynamically passive quantities in the Batchelo r regime of a smooth in space velocity field. For the case of arbitrary tem poral correlations of the velocity, we formulate the statistics of relevant characteristics of Lagrangian motion. This allows us to generalize many re sults obtained previously for strain delta correlated in time, thus answeri ng a question about the universality of these results. [S1063-651X(99)12810 -1].