Comparison of backwards and forwards relative dispersion in turbulence

We use Lagrangian stochastic models and direct numerical simulation for stationary isotropic turbulence to calculate backwards relative dispersion statistics, that is, the statistics of the earlier locations of particle pairs that at a later time are located at prescribed locations. We find that, in general, backwards relative dispersion proceeds at a much faster rate than relative dispersion forwards in time, and the difference between the two is sensitive to the nature of the flow field. The difference vanishes for Gaussian flows and for white-noise (in time) flows (for which relative dispersion can be described by a diffusion equation), suggesting that theories such as two-point closure and kinematic simulation do not differentiate between backwards and forwards dispersion. Backwards relative dispersion is very sensitive to the details of the tails of the probability density function for the Eulerian velocity difference between two points.