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Extra resources for Accretion Disks and Magnetic Fields in Astrophysics: Proceedings of the European Physical Society Study Conference, Held in Noto (Sicily), Italy, June 16–21, 1988

Example text

3. 1. po is a steady stream functionj '" is the magnitude ratio of magnetic field to velocity field in the corotating reference frame.

196, 323-344. J. 1967 Numerical study of two fluid Rayleigh-Taylor instability. Phys. Fluids 10, 297-307. HUGHES, D. W. & CATTANEO, F. 1987 A new look at the instability of a stratified horizontal magnetic field. Geophys. Astrophys. Fluid Dyn. 39, 65-8l. K. 1983 Transport effects associated with turbulence with particular attention to the influence of helicity. Rep. Prog. Phys. 46, 621-664. N. 1975 The generation of magnetic fields in astrophysical bodies. X. Magnetic buoyancy and the solar dynamo.

Mathematical Formulation As explained ab ove , we have considered an initial state consisting of a region of uniform horizontal magnetic field embedded in a field-free, convectively stable atmosphere. This of course is not a true equilibrium since, for any finite value of the magnetic diffusivity 1), the magnetic diffusion equation (1)V' 2 B = 0) is not satisfied ac ross the interfaces of the magnetic field. However, this is not a serious problem provided that the instabilities grow on a time scale which is much shorter than that on which the field diffuses appreciably - this may be checked aposteriori and, fortunately, does indeed turn out to be true.

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