TURBULENCE-INDUCED RELATIVE VELOCITY OF DUST PARTICLES. I. IDENTICAL PARTICLES

We study the relative velocity of inertial particles suspended in turbulent flows and discuss implications for dust particle collisions in protoplanetary disks. We simulate a weakly compressible turbulent flow, evolving 14 particle species with friction timescale, tau(p), covering the entire range of scales in the flow. The particle Stokes numbers, St, measuring the ratio of tau(p) to the Kolmogorov timescale, are in the range 0.1 less than or similar to St less than or similar to 800. Using simulation results, we show that the model by Pan & Padoan gives satisfactory predictions for the rms relative velocity between identical particles. The probability distribution function (PDF) of the relative velocity is found to be highly non-Gaussian. The PDF tails are well described by a 4/3 stretched exponential function for particles with tau(p) similar or equal to 1-2 T-L, where T-L is the Lagrangian correlation timescale, consistent with a prediction based on PP10. The PDF approaches Gaussian only for very large particles with tau(p) greater than or similar to 54 T-L. We split particle pairs at given distances into two types with low and high relative speeds, referred to as continuous and caustic types, respectively, and compute their contributions to the collision kernel. Although amplified by the effect of clustering, the continuous contribution vanishes in the limit of infinitesimal particle distance, where the caustic contribution dominates. The caustic kernel per unit cross section rises rapidly as St increases toward similar or equal to 1, reaches a maximum at tau(p) similar or equal to 2 T-L, and decreases as tau(-1/2)(p) for tau(p) >> T-L.