Dust Sedimentation and Self‐sustained Kelvin‐Helmholtz Turbulence in Protoplanetary Disk Midplanes

Abstract

We perform numerical simulations of the Kelvin-Helmholtz instabilityin the midplane of a protoplanetary disk. A two-dimensional corotatingslice in the azimuthal - vertical plane of the disk is considered,where we include the Coriolis force and the radial advection of theKeplerian rotation flow. Dust grains, treated as individual particles,move under the influence of friction with the gas, while the gasis treated as a compressible fluid. The friction force from the dustgrains on the gas leads to a vertical shear in the gas rotation velocity.As the particles settle around the midplane due to gravity, the shearincreases, and eventually the flow becomes unstable to the Kelvin-Helmholtzinstability. The Kelvin-Helmholtz turbulence saturates when the verticalsettling of the dust is balanced by the turbulent diffusion awayfrom the midplane. The azimuthally averaged state of the self-sustainedKelvin-Helmholtz turbulence is found to have a constant Richardsonnumber in the region around the midplane where the dust-to-gas ratiois significant. Nevertheless, the dust density has a strong nonaxisymmetriccomponent. We identify a powerful clumping mechanism, caused by thedependence of the rotation velocity of the dust grains on the dust-to-gasratio, as the source of the nonaxisymmetry. Our simulations confirmrecent findings that the critical Richardson number for Kelvin-Helmholtzinstability is around unity or larger, rather than the classicalvalue of 1/4.