Shear instabilities in the dust layer of the solar nebula II. Different unperturbed states

In the previous paper (Sekiya and Ishitsu, 2000), the shear instability in the dust layer of the solar nebula was investigated by using the constant R ichardson number solution (Sekiya, 1998) as the unperturbed state, and the growth rate of the most unstable mode was calculated to be much less than t he Keplerian angular velocity as long as the Richardson number was larger t han 0.1. In this paper, we calculate the growth rate using different unpert urbed states: (1) a sinusoidal density distribution, and (2) a constant den sity around the midplane with sinusoidal transition regions. An unperturbed state of this paper is considered to correspond to the first stage of shea r instability that occurs as a result of dust settling in a laminar phase o f the solar nebula. On the other hand, the unperturbed state of the previou s paper corresponds to the quasi-equilibrium state (Sekiya, 1998) which is attained by the turbulent mixing. The results show that the growth rate is much larger than the Keplerian angular velocity, in contrast to the previou s result.