The streaming instability and Kelvin-Helmholtz instability are considered the two major sources causing clumping of dust particles and turbulence in the dust layer of a protoplanetary disk as long as we consider the dead zone where the magneto-rotational instability does not grow. Extensive numerical simulations have been carried out in order to elucidate the condition for the development of particle clumping caused by the streaming instability. In this paper, a set of two parameters suitable for classifying the numerical results is proposed. One is the Stokes number that has been employed in previous works and the other is the dust particle column density that is nondimensionalized using the gas density in the midplane, Keplerian angular velocity, and difference between the Keplerian and gaseous orbital velocities. The magnitude of dust clumping is a measure of the behavior of the dust layer. Using three-dimensional numerical simulations of dust particles and gas based on Athena code v. 4.2, it is confirmed that the magnitude of dust clumping for two disk models are similar if the corresponding sets of values of the two parameters are identical to each other, even if the values of the metallicity (i.e., the ratio of the columns density of the dust particles to that of the gas) are different.

We investigate the effect of a radial pressure bump in a protoplanetary disk on planetesimal formation. We performed the two-dimensional numerical simulation of the dynamical interaction of solid particles and gas with an initially defined pressure bump under the assumption of axisymmetry. The aim of this work is to elucidate the effects of the stellar vertical gravity that were omitted in a previous study. Our results are very different from the previous study, which omitted the vertical gravity. Because dust particles settle toward the midplane because of the vertical gravity to form a thin dust layer, the regions outside of the dust layer are scarcely affected by the back-reaction of the dust. Hence, the gas column density keeps its initial profile with a bump, and dust particles migrate toward the bump. In addition, the turbulence due to the Kelvin-Helmholtz instability caused by the difference of the azimuthal velocities between the inside and outside of the dust layer is suppressed where the radial pressure gradient is reduced by the pressure bump. The dust settling proceeds further where the turbulence is weak, and a number of dust clumps are formed. The dust density in some clumps exceeds the Roche density. Planetesimals are considered to be formed from these clumps owing to the self-gravity.