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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
Earth, Planets and Space volume 52, pages 517–526 (2000)
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.
Champney, J. M., A. R. Dobrovolskis, and J. N. Cuzzi, A numerical turbulence model for multiphase flows in the protoplanetary nebula, Phys. Fluids, 7, 1703–1711, 1995.
Chandrasekhar, S., Hydrodynamic and Hydromagnetic Stability, 652 pp., Oxford Univ. Press, Oxford, 1961.
Coradini, A., C. Federico, and G. Magni, Formation of planetesimals in an evolving protoplanetary disk, Astron. Astrophys., 98, 173–185, 1981.
Cuzzi, J. N., A. R. Dobrovolskis, and J. M. Champney, Particle-gas dynamics in the midplane of a protoplanetary nebula, Icarus, 106, 102–134, 1993.
Goldreich, P. and W. R. Ward, The formation of planetesimals, Astrophys. J., 183, 1051–1061, 1973.
Howard, L. N., Note on a paper of John W. Miles, J. Fluid Mech., 10, 509–512, 1961.
Lin, C. C., The Theory of Hydrodynamic Stability, 155 pp., Cambridge Univ. Press, 1955.
Nakagawa, Y., K. Nakazawa, and C. Hayashi, Growth and sedimentation of dust grains in the primordial solar nebula, Icarus, 45, 517–528, 1981.
Nakagawa, Y., M. Sekiya, and C. Hayashi, Settling and growth of dust particles in a laminar phase of a low-mass solar nebula, Icarus, 67, 375–390, 1986.
Safronov, V. S., Evolution of the Protoplanetary Cloud and Formation of the Earth and the Planets, 206 pp., Nauka, Moscow, [NASA Tech. Trans. F-677], 1969.
Sekiya, M., Gravitational instabilities in a dust-gas layer and formation of planetesimals in the solar nebula, Progr. Theor. Phys., 69, 1116–1130, 1983.
Sekiya, M., Quasi-equilibrium density distributions of small dust aggregations in the solar nebula, Icarus, 133, 298–309, 1998.
Weidenschilling, S. J., Dust to planetesimals: Settling and coagulation in the solar nebula, Icarus, 44, 172–189, 1980.
Weidenschilling, S. J., Evolutionofgrains in a turbulent solar nebula, Icarus, 60, 553–567, 1984.
Weidenschilling, S. J. and J. N. Cuzzi, Formation of planetesimals in the solar nebula, in Protostars and Planets III, edited by E. H. Levy and J. I. Lunine, pp. 1031–1060. Univ. of Arizona Press, Tucson, 1993.
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Sekiya, M., Ishitsu, N. 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. Earth Planet Sp 52, 517–526 (2000). https://doi.org/10.1186/BF03351656
- Coriolis Force
- Richardson Number
- Shear Instability
- Solar Nebula