Abstract
A spectral method is used to explore the nonlinear evolution of known linear instabilities in a 2D differentially rotating magneto-hydrodynamic shell, representing the solar tachocline. Several simulations are presented, with a range of outcomes for the magnetic field configuration. Most spectacularly, the `clam instability', which occurs for solar differential rotation and a strong broad toroidal magnetic field structure, results in the field tipping over by 90° and reconnecting. A common characteristic of all the simulations though is that the nonlinear instabilities produce a strong angular momentum mixing effect which pushes the rotation towards a solid body form. It is argued that this may be the mechanism required by the model of Spiegel and Zahn to limit the tachocline's thickness.
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Brown, T. M., Christensen-Dalsgaard, J., Dziembowski, W. A., Goode, P. R., Gough, D. O., and Morrow, C. A.: 1989, Astrophys. J 343, 526.
Canuto, C., Hussaini, M. Y., Quarteroni, A., and Zang, T. A.: 1988, Spectral Methods in Fluid Dynamics, Springer-Verlag, Berlin.
Charbonneau, P. and MacGregor, K. B.: 1997, Astrophys. J. 486, 502.
Charbonneau, P., Dikpati, M., and Gilman, P. A.: 1999, Astrophys. J. 526, 523.
Charbonneau, P., Tomczyk, S., Schou, J., and Thompson, M. J.: 1998, Astrophys. J. 496, 1015.
Charbonneau, P., Christensen-Dalsgaard, J., Henning, R., Larsen, R. M., Schou, J., Thompson, M. J., and Tomczyk, S.: 1999, Astrophys. J. 527, 445.
Dahlburg, J. P., Montgomery, D., and Matthaeus, W. H.: 1985, J. Plasma Phys. 34, 1.
de Toma, G., White, O. R., and Harvey, K.: 2000, Astrophys. J. 529, 1101.
Dikpati, M. and Gilman, P. A.: 1999, Astrophys. J. 512, 417.
Dikpati, M. and Gilman, P. A.: 2000, Astrophys. J., to appear.
Dziembowski, W. and Kosovichev, A.: 1987, Acta Astron. 37, 341.
Gilman, P. A.: 2000, Solar Phys. 192, 27.
Gilman, P. A. and Dikpati, M.: 2000, Astrophys. J. 528, 552.
Gilman, P. A. and Fox, P. A.: 1997, Astrophys. J. 484, 439.
Gilman, P. A. and Fox, P. A.: 1999a, Astrophys. J. 510, 1018.
Gilman, P. A. and Fox, P. A.: 1999b, Astrophys. J. 522, 1167.
Golub, G. H. and van Loan, C. F.: 1989, Matrix Computations, 2nd ed., Johns Hopkins University Press, Baltimore.
Jackson, J. D.: 1975, Classical Electrodynamics, 2nd ed., John Wiley and Sons, New York, p. 100.
Jameson, A., Schmidt, H., and Turkel, E.: 1981, AIAA pap. no. 81-259.
Machenhauer, B.: 1979, Numerical Methods used in Atmospheric Models, Vol. II, GARP publ. series No. 17, World Meteorological Organization, p. 124.
Parker, E. N.: 1993, Astrophys. J. 408, 707.
Schüssler, M.: 1996, in K. C. Tsinganos (ed.), Solar and Astrophysical MHD Flows,NATOASI Ser. C, 481, Kluwer Academic Publishers, Dordrecht, p. 17.
Spiegel, E. A. and Zahn, J.-P.: 1992, Astron. Astrophys. 265, 106.
Tomczyk, S., Schou, J., and Thompson, M. J.: 1995, Astrophys. J. 448, L57.
Watson, M.: 1981, Geophys. Astrophys. Fluid Dyn. 16, 285.
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Cally, P. Nonlinear Evolution of 2d Tachocline Instabilities. Solar Physics 199, 231–249 (2001). https://doi.org/10.1023/A:1010390814663
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DOI: https://doi.org/10.1023/A:1010390814663