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

Abstract

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 Richardson number solution (Sekiya, 1998) as the unperturbed state, and the growth rate of the most unstable mode was calculated to be much less than the Keplerian angular velocity as long as the Richardson number was larger than 0.1. In this paper, we calculate the growth rate using different unperturbed states: (1) a sinusoidal density distribution, and (2) a constant density around the midplane with sinusoidal transition regions. An unperturbed state of this paper is considered to correspond to the first stage of shear instability that occurs as a result of dust settling in a laminar phase of the solar nebula. On the other hand, the unperturbed state of the previous 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 previous result.

Shear instabilities in the dust layer of the solar nebula III. Effects of the Coriolis force

“…However, the shear instability in the dust layer is not understood enough. In order to elucidate the nature of the shear-induced instability, we have performed linear calculations of the perturbation equations of the fluid mechanics in previous papers Ishitsu, 2000 and2001, hereafter referred to as Papers I and II, respectively) under the following assumptions: (1) The self-gravity is neglected. (2) A mixture of gas and dust is treated as one fluid, which is a good approximation in the case where dust aggregate sizes are small ( 1 cm).…”

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In previous our papers ( Ishitsu, 2000 and2001), hydrodynamic stability of the dust layer in the solar nebula is investigated. However, these papers neglected the rotational effects, that is, the Coriolis and tidal forces.

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The Possibility of the Kelvin–Helmholtz Instability during Sedimentation of Dust Grains in the Protoplanetary Disk

“…Assuming equilibrium condition for KHI, previous studies have shown that GI tends to occur if dust abundance in the protoplanetary disk is much larger than MMSN model (Sekiya 1998;Sekiya & Ishitsu 2001). Now using non-equilibrium time dependent density profile during sedimentation, we consider the possibility for GI in the case with large f d .…”

“…Under the local maximum point, the Rayleigh-Taylor instability (RTI) is suspected to occur because the distribution of the gradient of dust density becomes positive (Chandrasekhar 1961). If RTI occurs, the distribution of dust density in this region is expected to be adjusted as to be constant (Sekiya & Ishitsu 2001). If it is assumed that the growth rate of RTI is larger than that of KHI, and that the distribution of dust density becomes constant around the midplane, the gradient of dust density becomes zero near the midplane.…”

Kelvin–Helmholtz instabilities in multi-sized dust layers

“…However, vertical gradient of dust abundance is indicated to induce the vertical shear of the azimuthal velocity (Cuzzi et al 1993;Sekiya 1998), and the shear is expected to induce the Kelvin-Helmholtz instability (KHI) (Chandrasekhar 1961). KHI is expected to induce shear-driven turbulence that prevents dust aggregates from settling for GI (Cuzzi et al 1993;Sekiya 1998;Sekiya & Ishitsu 2001;Michikoshi & Inutsuka 2006). Previous studies indicate that GI tends to be occur when dust abundance is high (Sekiya 1998;Johansen & Youdin 2007).…”