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Periodic and Aperiodic Behaviour in Stellar Dynamos

Published online by Cambridge University Press:  04 August 2017

F. Cattaneo ,
C.A. Jones  and
N.O. Weiss
F. Cattaneo
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England
C.A. Jones
Affiliation:
School of Mathematics, University of Newcastle-upon-Tyne, England
N.O. Weiss
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England

Abstract

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We have constructed a simple parametrized mean field dynamo model that includes the dynamical interaction between the magnetic field and differential rotation. This system of seven coupled nonlinear ordinary differential equations has finite amplitude oscillatory solutions (corresponding to Parker's dynamo waves) when the dynamo number D>1. We have studied two regimes. In the first, the velocity shear is reduced by the Lorentz force and there are stable periodic solutions for all D>1. In the second there is a transition from strictly periodic oscillations to aperiodic (chaotic) behaviour as D is increased. This simple example shows that nonlinear hydromagnetic dynamos can produce aperiodic cycles, with Maunder minima, as observed in the sun and other late-type stars.

Type
III. Theory of Stellar Magnetic Field Generation
Information
Symposium - International Astronomical Union , Volume 102: Solar and Stellar Magnetic Fields: Origins and Coronal Effects , 1983 , pp. 307 - 310
Copyright
Copyright © Reidel 1983 

References

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