Shear instabilities in the dust layer of the solar nebula III. Effects of the Coriolis force
Earth, Planets and Space volume 54, pages 917–926 (2002)
In previous our papers (Sekiya and Ishitsu, 2000 and 2001), 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. These forces may stabilize the shear instability of the dust layer. In this paper, the linear stability analysis with the Coriolis and without tidal force is done in order to elucidate the effects of the Coriolis force. Our results indicate that the growth rates of the instabilities are similar between the cases with and without the Coriolis force. However, we found a new type of instability which resembles the Lindblad resonance. This instability only emerges if the growth rate is similar to or smaller than the Keplerian angular frequency. The energy source of the instability is different from that of the shear instability.
Adachi, I., C. Hayashi, and K. Nakazawa, The gas drag effect on the elliptical motion of a solid body in the primordial solar nebula, Prog. Theor. Phys., 56, 1756–1771, 1976.
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.
Coradini, A., C. Frederico, and G. Magni, Formation of planetesimals in an evolving protoplanetary disk, Astron. Astrophys., 98, 173–185, 1981.
Cuzzi, J. N., A. R. Doborvolskis, and J. M. Champney, Particle-gas dynamics in the midplane of a protoplanetary nebula, Icarus, 106, 102–134, 1993.
Dobrovolskis, A. R., J. S. Dacles-Mariani, and J. N. Cuzzi, Production and damping of turbulence by particles in the solar nebula, J. Geophys. Res., 104(E21), 30805–30815, 1999.
Drazin, P. G. and W. H. Reid, Hydrodynamic Stability, Cambridge Univ. Press, 1981.
Goldreich, P. and W. R. Ward, The formation of planetesimals, Astrophys. J., 183, 1051–1061, 1973.
Hayashi, C., Structure of the solar nebula, growth and decay of magnetic fields and effects of magnetic and turbulent viscosities on the nebula, Progr. Theor. Phys. Suppl., 70, 35–53, 1981.
Hayashi, C., K. Nakazawa, and Y. Nakagawa, Formation of the solar system, in Protostars and Planets II, edited by B. C. Black and M. S. Matthews, pp. 1100–1153, Univ. of Arizona Press, Tucson, 1985.
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, Nauka, Moscow, [NASA Tech. Trans. F-677], 1969.
Sekiya, M., Gravitational instability 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, 298–303, 1998.
Sekiya, M. and N. Ishitsu, 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 Space, 52, 517–526, 2000.
Sekiya, M. and N. Ishitsu, Shear instabilities in the dust layer of the solar nebula II. Different unperturbed states, Earth Planets Space, 53, 761–765, 2001.
Shu, F. H., The Physics of Astrophysics II. Gas Dynamics, University Science Books, 1992.
Watanabe, S. and T. Yamada, Numerical simulations of dust-gas 2-phase flows in the solar nebula, Eos, Trans. Am. Geoph. Union Suppl., 81, No. 22, WP99, 2000.
Weidenschilling, S. J., Dust to planetesimals: settling and coagulation in the solar nebula, Icarus, 44, 172–189, 1980.
Weidenschilling, S. J., Evolution of grains 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.
About this article
Cite this article
Ishitsu, N., Sekiya, M. Shear instabilities in the dust layer of the solar nebula III. Effects of the Coriolis force. Earth Planet Sp 54, 917–926 (2002). https://doi.org/10.1186/BF03352439