Single and two-particle motion of heavy particles in turbulence

We study motion of small particles in turbulence when the particle relaxation time falls in the range of inertial time-scales of the flow. Due to inertia, particles drift relative to the fluid. We show that the drift velocity is close to the Lagrangian velocity increments of turbulence at the particle relaxation time. We demonstrate that the collective drift of two close particles makes them see local velocity increments fluctuate fast and we introduce the corresponding Langevin description for separation dynamics. This allows to describe the behavior of the Lyapunov exponent and give the analogue of Richardson's law for separation above viscous scale.