Variable-range projection model for turbulence-driven collisions

We discuss the relative speeds DeltaV of inertial particles suspended in a highly turbulent gas when the Stokes number, a dimensionless measure of their inertia, is large. We identify a mechanism giving rise to the distribution P(DeltaV) approximately exp(-C|DeltaV|(4/3)) (for some constant C). Our conclusions are supported by numerical simulations, and by the analytical solution of a model equation of motion. The results determine the rate of collisions between suspended particles. They are relevant to the hypothesized mechanism for formation of planets by aggregation of dust particles in circumstellar nebula.