1305.0307 (Liubin Pan et al.)

Turbulence-Induced Relative Velocity of Dust Particles I: Identical Particles    [PDF]

Liubin Pan, Paolo Padoan

We study the relative velocity of inertial particles suspended in turbulent flows and discuss implications for dust particle collisions in protoplanetay disks. We simulate a weakly compressible turbulent flow at 512^3 and evolve 14 species of particles with different friction timescales, tau_p. The Stoke number, St, of the smallest particles is ~0.1, where St is the ratio of tau_p to the Kolmorgorov timescale, while the largest particles have tau_p =54T_L, where T_L is the flow Lagrangian correlation timescale. We find that the model by Pan & Padoan (PP10) gives satisfactory predictions for the rms relative velocity between identical particles. The model shows that the relative velocity of two same-size particles is determined by the particle memory of the flow velocity difference along their trajectories, and thus depends on the particle pair separation backward in time. We compute the collision kernel accounting for the effect of turbulent clustering. The kernel per unit cross section shows an abrupt rise as St increases toward ~1, corresponding the rapid caustic formation. At St>1, the kernel first increases slightly, peaks at tau_ p~2T_L, and finally decreases as tau_p^-1/2 for tau_p>>T_L. The probability distribution function (PDF) of the particle relative velocity is highly non-Gaussian. We identify two sources of non-Gaussianity: the imprint of the turbulent intermittency and an intrinsic contribution from the particle dynamics. The PDF is fattest at St~1. The PDF tails for particles with tau_p=1-2T_L are well described by a 4/3 stretched exponential function, consistent with a prediction using the physical picture of PP10. The PDF approaches Gaussian only for very large particles with tau_p>~54T_L. Coagulation models of dust particle evolution in protoplanetary disks should account for the new features of the collision kernel and the non-Gaussianity of the collision velocity.

View original: http://arxiv.org/abs/1305.0307