Dust sedimentation and self-sustained Kelvin-Helmholtz turbulence in protoplanetary disk midplanes

We perform numerical simulations of the Kelvin-Helmholtz instability in the midplane of a protoplanetary disk. A two-dimensional corotating slice in the azimuthal - vertical plane of the disk is considered, where we include the Coriolis force and the radial advection of the Keplerian rotation flow. Dust grains, treated as individual particles, move under the influence of friction with the gas, while the gas is treated as a compressible fluid. The friction force from the dust grains on the gas leads to a vertical shear in the gas rotation velocity. As the particles settle around the midplane due to gravity, the shear increases, and eventually the flow becomes unstable to the Kelvin-Helmholtz instability. The Kelvin-Helmholtz turbulence saturates when the vertical settling of the dust is balanced by the turbulent diffusion away from the midplane. The azimuthally averaged state of the self-sustained Kelvin-Helmholtz turbulence is found to have a constant Richardson number in the region around the midplane where the dust-to-gas ratio is significant. Nevertheless, the dust density has a strong nonaxisymmetric component. We identify a powerful clumping mechanism, caused by the dependence of the rotation velocity of the dust grains on the dust-to-gas ratio, as the source of the nonaxisymmetry. Our simulations confirm recent findings that the critical Richardson number for Kelvin-Helmholtz instability is around unity or larger, rather than the classical value of 1/4.