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


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.


  1. 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.

    Article  Google Scholar 

  2. 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.

    Article  Google Scholar 

  3. Coradini, A., C. Frederico, and G. Magni, Formation of planetesimals in an evolving protoplanetary disk, Astron. Astrophys., 98, 173–185, 1981.

    Google Scholar 

  4. 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.

    Article  Google Scholar 

  5. 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.

    Article  Google Scholar 

  6. Drazin, P. G. and W. H. Reid, Hydrodynamic Stability, Cambridge Univ. Press, 1981.

  7. Goldreich, P. and W. R. Ward, The formation of planetesimals, Astrophys. J., 183, 1051–1061, 1973.

    Article  Google Scholar 

  8. 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.

    Article  Google Scholar 

  9. 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.

    Google Scholar 

  10. Nakagawa, Y., K. Nakazawa, and C. Hayashi, Growth and sedimentation of dust grains in the primordial solar nebula, Icarus, 45, 517–528, 1981.

    Article  Google Scholar 

  11. 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.

    Article  Google Scholar 

  12. Safronov, V. S., Evolution of the Protoplanetary Cloud and Formation of the Earth and the Planets, Nauka, Moscow, [NASA Tech. Trans. F-677], 1969.

  13. Sekiya, M., Gravitational instability in a dust-gas layer and formation of planetesimals in the solar nebula, Progr. Theor. Phys., 69, 1116–1130, 1983.

    Article  Google Scholar 

  14. Sekiya, M., Quasi-equilibrium density distributions of small dust aggregations in the solar nebula, Icarus, 133, 298–303, 1998.

    Article  Google Scholar 

  15. 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.

    Article  Google Scholar 

  16. 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.

    Article  Google Scholar 

  17. Shu, F. H., The Physics of Astrophysics II. Gas Dynamics, University Science Books, 1992.

  18. 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.

    Google Scholar 

  19. Weidenschilling, S. J., Dust to planetesimals: settling and coagulation in the solar nebula, Icarus, 44, 172–189, 1980.

    Article  Google Scholar 

  20. Weidenschilling, S. J., Evolution of grains in a turbulent solar nebula, Icarus, 60, 553–567, 1984.

    Article  Google Scholar 

  21. 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.

    Google Scholar 

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Correspondence to Naoki Ishitsu.

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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).

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  • Dust
  • Coriolis Force
  • Vertical Shear
  • Tidal Force
  • Shear Instability