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Turbulence is the dominant source of collisional velocities for grains with awide range of sizes in protoplanetary disks. So far, only Kolmogorov turbulencehas been considered for calculating grain collisional velocities, despite theevidence that turbulence in protoplanetary disks may be non-Kolmogorov. In thiswork, we present calculations of grain collisional velocities for arbitraryturbulence models characterized by power-law spectra and determined by threedimensionless parameters: the slope of the kinetic energy spectrum, the slopeof the auto-correlation time, and the Reynolds number. The implications of ourresults are illustrated by numerical simulations of the grain size evolutionfor different turbulence models. We find that for the modeled cases of theIroshnikov-Kraichnan turbulence and the turbulence induced by themagneto-rotational instabilities, collisional velocities of small grains aremuch larger than those for the standard Kolmogorov turbulence. This leads tofaster grain coagulation in the outer regions of protoplanetary disks,resulting in rapid increase of dust opacity in mm-wavelength and possiblypromoting planet formation in very young disks.

Impact of magneto-rotational instability on grain growth in protoplanetary disks: II. Increased grain collisional velocities