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Astron. Astrophys. 345, 669-679 (1999)

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The influence of geometry and topology on axisymmetric mean-field dynamos

Eurico Covas 1, Reza Tavakol 1, Andrew Tworkowski 2, Axel Brandenburg 3, John Brooke 4 and David Moss 5

1 Astronomy Unit, School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London E1 4NS, UK
(eoc; reza@maths.qmw.ac.uk)
2 Mathematical Research Centre, School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London E1 4NS, UK (A.S.Tworkowski@qmw.ac.uk)
3 Department of Mathematics, University of Newcastle upon Tyne NE1 7RU, UK (Axel.Brandenburg@ncl.ac.uk)
4 Manchester Computing, The University, Manchester M13 9PL, UK (zzalsjb@afs.mcc.ac.uk)
5 Department of Mathematics, The University, Manchester M13 9PL, UK (moss@ma.man.ac.uk)

Received 9 November 1998 / Accepted 8 February 1999


We study the changes in the dynamical behaviour of axisymmetric spherical mean-field dynamo models produced by changes in their geometry and topology, by considering a two parameter family of models, ranging from a full sphere to spherical shell, torus and disc-like configurations, within a unified framework. We find that the two parameter space of the family of models considered here separates into at least three different regions with distinct characteristics for the onset of dynamo action. In two of these regions, the most easily excited fields are oscillatory, in one case with dipolar symmetry, and in the other with quadrupolar, whereas in the third region the most easily excited field is steady and quadrupolar. In the nonlinear regime, we find that topological changes can alter significantly the dynamical behaviour, whilst modest changes in geometry can produce qualitative changes, particularly for thin disc-like configurations. This is of potential importance, since the exact shapes of astrophysical bodies, especially accretion discs and galaxies, are usually not precisely known.

Key words: accretion, accretion disks – chaos – magnetic fields – Magnetohydrodynamics (MHD) – Sun: magnetic fields

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© European Southern Observatory (ESO) 1999

Online publication: April 19, 1999