Particle and particle pair dispersion in turbulence modeled with spatially and temporally correlated stochastic processes.

In this paper we present a model for modeling the diffusion and relative dispersion of particles in homogeneous isotropic turbulence. We use a Heisenberg-like Hamiltonian to incorporate spatial correlations between fluid particles, which are modeled by stochastic processes correlated in time. We are able to reproduce the ballistic regime in the mean square displacement of single particles and the transition to a normal diffusion regime for long times. For the dispersion of particle pairs we find a t2 dependence of the mean square separation at short times and a t dependence for long ones. For intermediate times indications for a Richardson t3 law are observed in certain situations. Finally, the influence of inertia of real particles on the dispersion is investigated.