Shear instabilities in the dust layer of the solar nebula I. The linear analysis of a non-gravitating one-fluid model without the Coriolis and the solar tidal forces

Minoru Sekiya, Naoki Ishitsu

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

As dust aggregates settled toward the midplane of the solar nebula, a thin dust layer was formed. The rotational velocity was a function of the distance from the midplane in this layer, and the shear induced turbulence might occur, which prevented the dust aggregates from settling further toward the midplane. Thus, it was difficult for the dust density on the midplane to exceed the critical density of the gravitational stability. In this paper, the linear analysis of the shear instability is made under the following assumptions: The self-gravity, the solar tidal force (thus the Keplerian shear), and the Coriolis force are neglected; the unperturbed state has a constant Richardson's number in the dust layer; further we restrict ourselves to the case where dust aggregates are small enough, and a mixture of dust and gas is treated as one fluid. Numerical results show that the growth rate of the most unstable mode is much less than the Keplerian angular frequency, as long as the Richardson number is larger than 0.1.

Original languageEnglish
Pages (from-to)517-526
Number of pages10
Journalearth, planets and space
Volume52
Issue number7
DOIs
Publication statusPublished - Aug 1 2000

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solar nebula
dust
shear
fluid
fluids
Richardson number
Coriolis force
settling
analysis
turbulence
gravity
gravitation
gases
gas

All Science Journal Classification (ASJC) codes

  • Geology
  • Space and Planetary Science

Cite this

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abstract = "As dust aggregates settled toward the midplane of the solar nebula, a thin dust layer was formed. The rotational velocity was a function of the distance from the midplane in this layer, and the shear induced turbulence might occur, which prevented the dust aggregates from settling further toward the midplane. Thus, it was difficult for the dust density on the midplane to exceed the critical density of the gravitational stability. In this paper, the linear analysis of the shear instability is made under the following assumptions: The self-gravity, the solar tidal force (thus the Keplerian shear), and the Coriolis force are neglected; the unperturbed state has a constant Richardson's number in the dust layer; further we restrict ourselves to the case where dust aggregates are small enough, and a mixture of dust and gas is treated as one fluid. Numerical results show that the growth rate of the most unstable mode is much less than the Keplerian angular frequency, as long as the Richardson number is larger than 0.1.",
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N2 - As dust aggregates settled toward the midplane of the solar nebula, a thin dust layer was formed. The rotational velocity was a function of the distance from the midplane in this layer, and the shear induced turbulence might occur, which prevented the dust aggregates from settling further toward the midplane. Thus, it was difficult for the dust density on the midplane to exceed the critical density of the gravitational stability. In this paper, the linear analysis of the shear instability is made under the following assumptions: The self-gravity, the solar tidal force (thus the Keplerian shear), and the Coriolis force are neglected; the unperturbed state has a constant Richardson's number in the dust layer; further we restrict ourselves to the case where dust aggregates are small enough, and a mixture of dust and gas is treated as one fluid. Numerical results show that the growth rate of the most unstable mode is much less than the Keplerian angular frequency, as long as the Richardson number is larger than 0.1.

AB - As dust aggregates settled toward the midplane of the solar nebula, a thin dust layer was formed. The rotational velocity was a function of the distance from the midplane in this layer, and the shear induced turbulence might occur, which prevented the dust aggregates from settling further toward the midplane. Thus, it was difficult for the dust density on the midplane to exceed the critical density of the gravitational stability. In this paper, the linear analysis of the shear instability is made under the following assumptions: The self-gravity, the solar tidal force (thus the Keplerian shear), and the Coriolis force are neglected; the unperturbed state has a constant Richardson's number in the dust layer; further we restrict ourselves to the case where dust aggregates are small enough, and a mixture of dust and gas is treated as one fluid. Numerical results show that the growth rate of the most unstable mode is much less than the Keplerian angular frequency, as long as the Richardson number is larger than 0.1.

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