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

In this paper we present a new model for modeling the diffusion and relative dispersion of particles in homogeneous isotropic turbulence. We use an 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 squared displacement of single particles and the transition to a normal diffusion regime for long times. For the dispersion of particle pairs we find a $t^{2}$-dependence of the mean squared separation at short times and a $t$-dependence for long ones. For intermediate times indications for a Richardson $t^{3}$ law are observed in certain situations. Finally the influence of inertia of real particles on the dispersion is investigated.

Clustering of inelastic soft spheres in homogeneous turbulence

In this paper we numerically investigate the influence of dissipation during particle collisions in an homogeneous turbulent velocity field by coupling a discrete element method to a Lattice-Boltzmann simulation with spectral forcing. We show that even at moderate particle volume fractions the influence of dissipative collisions is important. We also investigate the transition from a regime where the turbulent velocity field significantly influences the spatial distribution of particles to a regime where the distribution is mainly influenced by particle collisions.