Gubbins, D., Barber, C.N., Gibbons, S. and Love, J.J. (2000) Kinematic dynamo action in a sphere. II. Symmetry selection. Proceedings of the Royal Society Series A: Mathematical Physical and Engineering Sciences, 456 (1999). pp. 16691683. ISSN 14712946

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Abstract
The magnetic fields of the planets are generated by dynamo action in their electrically conducting interiors. The Earth possesses an axial dipole magnetic field but other planets have other configurations: Uranus has an equatorial dipole for example. In a previous paper we explored a twoparameter class of flows, comprising convection rolls, differential rotation (D) and meridional circulation (M), for dynamo generation of steady fields with axial dipole symmetry by solving the kinematic dynamo equations. In this paper we explore generation of the remaining three allowed symmetries: axial quadrupole, equatorial dipole and equatorial quadrupole. The results have implications for the fully nonlinear dynamical dynamo because the flows qualitatively resemble those driven by thermal convection in a rotating sphere, and the symmetries define separable solutions of the nonlinear equations. Axial dipole solutions are generally preferred (they have lower critical magnetic Reynolds number) for D > 0, corresponding to westward surface drift. Axial quadrupoles are preferred for D < 0, and equatorial dipoles for convection with little D or M. No equatorial quadrupole solutions have been found. Symmetry selection can be understood if one assumes that the flow concentrates flux in certain places without reference to sign. Fields with dipole symmetry must change sign across the Equator; if flux is concentrated at the Equator, as tends to be the case for D < 0, they have a small lengthscale and consequent high dissipation, making them harder to generate than axial quadrupoles. If flux is concentrated nearer the poles (D > 0), axial dipoles are preferred. The equatorial dipole must change sign between east and west hemispheres, and is not favoured by any elongation of the flux in longitude (caused by D) or polar concentrations (caused by M): they are preferred for small D and M. Polar and equatorial concentrations can be related to dynamo waves and the sign of Parker's dynamo number. For the threedimensional flow considered here, the sign of the dynamo number is related to the sense of spiralling of the convection rolls, which must be the same as the surface drift
Item Type:  Article 

Copyright, Publisher and Additional Information:  Copyright © 2000 The Royal Society 
Keywords:  Kinematic Dynamo Geomagnetism Symmetry 
Institution:  The University of Leeds 
Academic Units:  The University of Leeds > Faculty of Environment (Leeds) > School of Earth and Environment (Leeds) 
Depositing User:  Repository Officer 
Date Deposited:  23 Mar 2005 
Last Modified:  06 Jun 2014 09:35 
Published Version:  http://www.journals.royalsoc.ac.uk/link.asp?id=pqk... 
Status:  Published 
Refereed:  Yes 
Identification Number:  10.1098/rspa.2000.0581 
URI:  http://eprints.whiterose.ac.uk/id/eprint/362 