  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.
