Journal Article

Turbulence-induced collisional velocities and density enhancements: large inertial range results from shell models

Alexander Hubbard

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 426, issue 1, pages 784-795
Published in print October 2012 | ISSN: 0035-8711
Published online October 2012 | e-ISSN: 1365-2966 | DOI:
Turbulence-induced collisional velocities and density enhancements: large inertial range results from shell models

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To understand the earliest stages of planet formation, it is crucial to be able to predict the rate and the outcome of dust grains collisions, be it sticking and growth, bouncing or fragmentation. The outcome of such collisions depends on the collision speed, so we need a solid understanding of the rate and velocity distribution of turbulence-induced dust grain collisions. The rate of the collisions depends on both the speed of the collisions and the degree of clustering experienced by the dust grains, which is a known outcome of turbulence. We evolve the motion of dust grains in simulated turbulence, an approach that allows a large turbulent inertial range making it possible to investigate the effect of turbulence on meso-scale grains (millimetre and centimetre). We find three populations of dust grains: one highly clustered, cold and collisionless; one warm; and the third ‘hot’. Our results can be fitted by a simple formula, and predict both significantly slower typical collisional velocities for a given turbulent strength than previously considered, and modest effective clustering of the collisional populations, easing difficulties associated with bouncing and fragmentation barriers to dust grain growth. Nonetheless, the rate of high-velocity collisions falls off merely exponentially with relative velocity so some mid- or high-velocity collisions will still occur, promising some fragmentation.

Keywords: turbulence; planets and satellites: formation; protoplanetary discs

Journal Article.  9583 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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