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