Turbulenceinduced relative velocity of dust particles. III. The probability distribution
Motivated by its important role in the collisional growth of dust particles in protoplanetary disks, we investigate the probability distribution function (PDF) of the relative velocity of inertial particles suspended in turbulent flows. Using the simulation from our previous work, we compute the relative velocity PDF as a function of the friction timescales, τ{sub p1} and τ{sub p2}, of two particles of arbitrary sizes. The friction time of the particles included in the simulation ranges from 0.1τ{sub η} to 54T {sub L}, where τ{sub η} and T {sub L} are the Kolmogorov time and the Lagrangian correlation time of the flow, respectively. The relative velocity PDF is generically nonGaussian, exhibiting fat tails. For a fixed value of τ{sub p1}, the PDF shape is the fattest for equalsize particles (τ{sub p2} = τ{sub p1}), and becomes thinner at both τ{sub p2} < τ{sub p1} and τ{sub p2} > τ{sub p1}. Defining f as the friction time ratio of the smaller particle to the larger one, we find that, at a given f in (1/2) ≲ f ≲ 1, the PDF fatness first increases with the friction time τ{sub p,h} of the larger particle, peaks at τ{sub p,h} ≅ τ{sub η}, andmore »
 Authors:

^{[1]};
^{[2]};
^{[3]}
 HarvardSmithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States)
 ICREA and ICC, University of Barcelona, Marti i Franquès 1, E08028 Barcelona (Spain)
 Department of Astronomy, University of Texas, Austin, TX 78712 (United States)
 Publication Date:
 OSTI Identifier:
 22365171
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Astrophysical Journal; Journal Volume: 792; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ASTEROIDS; CORRELATIONS; DIFFUSION BARRIERS; DISTRIBUTION; DISTRIBUTION FUNCTIONS; DUSTS; FRAGMENTATION; LAGRANGIAN FUNCTION; PARTICLES; PLANETS; PROBABILITY; PROTOPLANETS; SATELLITES; SIMULATION; TURBULENCE; TURBULENT FLOW; VELOCITY