Protoplanetary Disk Turbulence Driven by the Streaming Instability: Nonlinear Saturation and Particle Concentration

Abstract

We present simulations of the non-linear evolution of streaming instabilities\nin protoplanetary disks. The two components of the disk, gas treated with grid\nhydrodynamics and solids treated as superparticles, are mutually coupled by\ndrag forces. We find that the initially laminar equilibrium flow spontaneously\ndevelops into turbulence in our unstratified local model. Marginally coupled\nsolids (that couple to the gas on a Keplerian time-scale) trigger an upward\ncascade to large particle clumps with peak overdensities above 100. The clumps\nevolve dynamically by losing material downstream to the radial drift flow while\nreceiving recycled material from upstream. Smaller, more tightly coupled solids\nproduce weaker turbulence with more transient overdensities on smaller length\nscales. The net inward radial drift is decreased for marginally coupled\nparticles, whereas the tightly coupled particles migrate faster in the\nsaturated turbulent state. The turbulent diffusion of solid particles, measured\nby their random walk, depends strongly on their stopping time and on the\nsolids-to-gas ratio of the background state, but diffusion is generally modest,\nparticularly for tightly coupled solids. Angular momentum transport is too weak\nand of the wrong sign to influence stellar accretion. Self-gravity and\ncollisions will be needed to determine the relevance of particle overdensities\nfor planetesimal formation.\n