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Magnetic instability in a rapidly rotating cylindrical annulus with a finitely conducting inner core
Authors:C J Lamb
Institution:Department of Mathematics , University of Glasgow, University Gardens , Glasgow , G12 8QW , Scotland , UK
Abstract:Abstract

We consider the stability of a toroidal magnetic field B = B(s*) /></span> (where (<i>s</i>*,φ,<i>z</i>*) are cylindrical polar coordinates) in a cylindrical annulus of conducting fluid with inner and outer radii <i>s<sub>i</sub> </i> and <i>s</i> <sub>o</sub> rotating rapidly about its axis. The outer boundary is taken to be either insulating or perfectly conducting, and the effect of a finite magnetic diffusivity in the inner core is investigated. The ratio of magnetic diffusivity in the inner core to that of the outer core is denoted by ηη→0 corresponding to a perfectly conducting inner core and η→∞ to an insulating one. Comparisons with the results of Fearn (1983b, 1988) were made and a good match found in the limits η→0 and η→∞ with his perfectly conducting and insulating results, respectively. In addition a new mode of instability was found in the eta;→0 regime. Features of this new mode are low frequency (both the frequency and growth rate →0 as η→0) and penetration deep into the inner core. Typically it is unstable at lower magnetic field strengths than the previously known instabilities.</td> </tr> <tr> <td align=
Keywords:Earth's core  magnetic instability  finitely conducting inner core
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