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Astron. Astrophys. 329, 350-360 (1998)

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Axisymmetric mean field dynamos
with dynamic and algebraic [FORMULA] -quenchings

Eurico Covas * 1, Reza Tavakol ** 1, Andrew Tworkowski *** 1 and Axel Brandenburg **** 2

1 Astronomy Unit, School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London E1 4NS, UK
2 Department of Mathematics, University of Newcastle upon Tyne NE1 7RU, UK

Received 5 May 1997 / Accepted 7 August 1997

Abstract

We study axisymmetric mean field spherical and spherical shell dynamo models, with both dynamic and algebraic [FORMULA] -quenchings. Our results show that there are qualitative as well as quantitative differences and similarities between these models. Regarding similarities, both groups of models exhibit symmetric, antisymmetric and mixed modes of behaviour. As regards differences, the important feature in the full sphere models is the occurrence of chaotic behaviour in the algebraic [FORMULA] -quenching models. For the spherical shell models with dynamic [FORMULA] the main features include the possibility of multi-attractor regimes with final state sensitivity with respect to small changes in the magnitude of [FORMULA] and the initial parity.

We find the effect of introducing a dynamic [FORMULA] is likely to be complicated and depend on the region of the parameter space considered, rather than a uniform change towards simplicity or complexity.

Key words: MHD – Sun: magnetic fields – stars: magnetic fields

* (E.O.Covas@qmw.ac.uk)
** (reza@maths.qmw.ac.uk)
*** (A.S.Tworkowski@qmw.ac.uk)
**** (Axel.Brandenburg@ncl.ac.uk)

Send offprint requests to: Eurico Covas

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© European Southern Observatory (ESO) 1998

Online publication: November 24, 1997
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