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

We present simulations of the non-linear evolution of streaming instabilitiesin protoplanetary disks. The two components of the disk, gas treated with gridhydrodynamics and solids treated as superparticles, are mutually coupled bydrag forces. We find that the initially laminar equilibrium flow spontaneouslydevelops into turbulence in our unstratified local model. Marginally coupledsolids (that couple to the gas on a Keplerian time-scale) trigger an upwardcascade to large particle clumps with peak overdensities above 100. The clumpsevolve dynamically by losing material downstream to the radial drift flow whilereceiving recycled material from upstream. Smaller, more tightly coupled solidsproduce weaker turbulence with more transient overdensities on smaller lengthscales. The net inward radial drift is decreased for marginally coupledparticles, whereas the tightly coupled particles migrate faster in thesaturated turbulent state. The turbulent diffusion of solid particles, measuredby their random walk, depends strongly on their stopping time and on thesolids-to-gas ratio of the background state, but diffusion is generally modest,particularly for tightly coupled solids. Angular momentum transport is too weakand of the wrong sign to influence stellar accretion. Self-gravity andcollisions will be needed to determine the relevance of particle overdensitiesfor planetesimal formation.