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Convective dynamo action in a spherical shell: symmetries and modulation

Published online by Cambridge University Press:  28 June 2016

Raphaël Raynaud  and
Steven M. Tobias
Raphaël Raynaud*
Affiliation:
School of Astronomy, Institute for Research in Fundamental Sciences (IPM), 19395-5531, Tehran, Iran LERMA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, École normale supérieure, F-75005, Paris, France
Steven M. Tobias
Affiliation:
Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK
*
†Email address for correspondence: raphael.raynaud@ipm.ir
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Abstract

We consider dynamo action driven by three-dimensional rotating anelastic convection in a spherical shell. Motivated by the behaviour of the solar dynamo, we examine the interaction of hydromagnetic modes with different symmetries and demonstrate how complicated interactions between convection, differential rotation and magnetic fields may lead to modulation of the basic cycle. For some parameters, type 1 modulation occurs by the transfer of energy between modes of different symmetries with little change in the overall amplitude; for other parameters, the modulation is of type 2, where the amplitude is significantly affected (leading to grand minima in activity) without significant changes in symmetry. Most importantly, we identify the presence of ‘supermodulation’ in the solutions, where the activity switches chaotically between type 1 and type 2 modulation; this is believed to be an important process in solar activity.

JFM classification

Convection: Convection MHD and Electrohydrodynamics: MHD and Electrohydrodynamics

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Rapids
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Journal of Fluid Mechanics , Volume 799 , 25 July 2016 , R6
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© 2016 Cambridge University Press 

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