A Simple Phenomenological Model for Grain Clustering in Turbulence

Abstract

We propose a simple model for density fluctuations of aerodynamic grains, embedded in a turbulent, gravitating gas disk. The model combines a calculation for the behavior of a group of grains encountering a single turbulent eddy, with a hierarchical approximation of the eddy statistics. This makes analytic predictions for a range of quantities including: distributions of grain densities, power spectra and correlation functions of fluctuations, and maximum grain densities reached. We predict how these scale as a function of grain drag time t_stop, spatial scale, grain-to-gas mass ratio, strength of turbulence (alpha), and detailed disk properties. We test these against numerical simulations with various turbulence-driving mechanisms. The simulations agree well with the predictions, spanning t_stop*Omega ~ 1e-4 - 10, alpha ~ 1e-10 - 1e-2, and grain-to-gas mass ratio ~0-3. Results from 'turbulent concentration' simulations and laboratory experiments are also predicted as a special case. Vortices on a wide range of scales disperse and concentrate grains hierarchically. For small grains this is most efficient in eddies with turnover time comparable to the stopping time, but fluctuations are also damped by local gas-grain drift. For large grains, shear and gravity lead to a much broader range of eddy scales driving fluctuations, with most power on the largest scales. The grain density distribution has a log-Poisson shape, with fluctuations for large grains up to factors >1000. We provide simple analytic expressions for the predictions, and discuss implications for planetesimal formation, grain growth, and the structure of turbulence.

23 pages, 10 figures, updated to match accepted version. Text greatly expanded with additional derivations for new regimes, comparison to other analytic grain clustering models, more detailed comparison with experimental data

References in corpus (13)

• Particle Stirring in Turbulent Gas Disks: Including Orbital Oscillations
• The Density Probability Distribution in Compressible Isothermal Turbulence: Solenoidal versus Compressive Forcing
• Closed-form expressions for particle relative velocities induced by turbulence
• Towards planetesimals: dense chondrule clumps in the protoplanetary nebula
• On the universality of supersonic turbulence
• Planet formation bursts at the borders of the dead zone in 2D numerical simulations of circumstellar disks
• The density structure and star formation rate of non-isothermal polytropic turbulence
• Is the Scaling of Supersonic Turbulence Universal?
• Midplane sedimentation of large solid bodies in turbulent protoplanetary discs
• Turbulence-Induced Relative Velocity of Dust Particles I: Identical Particles
• Stochastic suspensions of heavy particles
• Kinematics of solid particles in a turbulent protoplanetary disc
• Caustics and Intermittency in Turbulent Suspensions of Heavy Particles

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