TY - JOUR

T1 - Instability of non-linear α2-dynamos

AU - Fearn, D. R.

AU - Rahman, M. M.

N1 - Funding Information:
We would like to thank Dr. R. Hollerbach for numerous helpful discussions and for providing us with his program. The comments of two referees have been very helpful in producing a clearer and more concise description of this work. Mohammad M. Rahman is grateful to Glasgow University and the ORS scheme for funding him through a research studentship.

PY - 2004/5/12

Y1 - 2004/5/12

N2 - 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 B̄ 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 α0, the strength of α. Above some critical value of α0, 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 α0, 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 B̄ with α0.

AB - 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 B̄ 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 α0, the strength of α. Above some critical value of α0, 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 α0, 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 B̄ with α0.

KW - Earth's core

KW - Magnetic instability

KW - Non-linear dynamo

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U2 - 10.1016/j.pepi.2003.12.010

DO - 10.1016/j.pepi.2003.12.010

M3 - Article

AN - SCOPUS:1842420479

VL - 142

SP - 101

EP - 112

JO - Physics of the Earth and Planetary Interiors

JF - Physics of the Earth and Planetary Interiors

SN - 0031-9201

IS - 1-2

ER -