Instability of non-linear α 2-dynamos

Abstract

Studies of the stability of prescribed magnetic fields in rapidly rotating systems have clearly demonstrated the relevance of the mechanism of magnetic field instability to the dynamics of planetary cores, see for example [Magnetic instabilities in rapidly rotating systems. In: Proctor, M.R.E., Matthews, P.C., Rucklidge, A.M. (Eds.), Solar and Planetary Dynamos. CUP, 1993, p. 59] The present study investigates the non-linear development of such instabilities and their feedback on the field generation process. The non-axisymmetric instability of a mean magnetic field B ̄ generated by a prescribed α-effect has been investigated in a rapidly rotating fluid spherical shell. The mean field drives a flow through the Lorentz force in the momentum equation and this flow feeds back on the field-generation process in the magnetic induction equation, equilibrating the field at some finite amplitude. This amplitude increases with α 0, the strength of α. Above some critical value of α 0, the mean field becomes unstable to a non-axisymmetric instability. The present work is the continuation of preliminary work by [Phys. Earth Planet. Inter. 134 (2002) 213] to higher values of α 0, and to a different, more realistic, form of α. We are particularly interested in how the instability affects the mean field generated. We find that instability can dramatically reduce the strength of the mean field and significantly constrains the growth of B ̄ with α 0.