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Kinematic dynamo action in a sphere. I. Effects of differential rotation and meridional circulation on solutions with axial dipole symmetry

Gubbins, D., Barber, C.N., Gibbons, S. and Love, J.J. (2000) Kinematic dynamo action in a sphere. I. Effects of differential rotation and meridional circulation on solutions with axial dipole symmetry. Proceedings of the Royal Society Series A: Mathematical Physical and Engineering Sciences, 456 (1998). pp. 1333-1353. ISSN 1471-2946

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A sphere containing electrically conducting fluid can generate a magnetic field by dynamo action, provided the flow is sufficiently complicated and vigorous. The dynamo mechanism is thought to sustain magnetic fields in planets and stars. The kinematic dynamo problem tests steady flows for magnetic instability, but rather few dynamos have been found so far because of severe numerical difficulties. Dynamo action might, therefore, be quite unusual, at least for large-scale steady flows. We address this question by testing a two-parameter class of flows for dynamo generation of magnetic fields containing an axial dipole. The class of flows includes two completely different types of known dynamos, one dominated by differential rotation (D) and one with none. We find that 36% of the flows in seven distinct zones in parameter space act as dynamos, while the remaining 64% either fail to generate this type of magnetic field or generate fields that are too small in scale to be resolved by our numerical method. The two previously known dynamo types lie in the same zone, and it is therefore possible to change the flow continuously from one to the other without losing dynamo action. Differential rotation is found to promote large-scale axisymmetric toroidal magnetic fields, while meridional circulation (M) promotes large-scale axisymmetric poloidal fields concentrated at high latitudes near the axis. Magnetic fields resembling that of the Earth are generated by D > 0, corresponding to westward flow at the surface, and M of either sign but not zero. Very few oscillatory solutions are found.

Item Type: Article
Copyright, Publisher and Additional Information: Copyright © 2000 The Royal Society
Keywords: kinematic dynamos, geomagnetism, eigenvalue problems
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: 04 Jun 2014 22:25
Published Version: http://www.journals.royalsoc.ac.uk/link.asp?id=q9t...
Status: Published
Refereed: Yes
Identification Number: 10.1098/rspa.2000.0565
URI: http://eprints.whiterose.ac.uk/id/eprint/361

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