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Helicity generation and subcritical behaviour in rapidly rotating dynamos

Published online by Cambridge University Press:  19 August 2011

Binod Sreenivasan  and
Chris A. Jones
Binod Sreenivasan
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology, Kanpur 208016, India
Chris A. Jones*
Affiliation:
Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK
*
†Email address for correspondence: C.A.Jones@maths.leeds.ac.uk,bsreeni@iitk.ac.in
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Abstract

Numerical dynamo models based on convection-driven flow in a rapidly rotating spherical shell frequently give rise to strong, stable, dipolar magnetic fields. Dipolar dynamos can be subcritical in the sense that strong magnetic fields are sustained at a Rayleigh number lower than that required for a dynamo to grow from a small seed field. In this paper we find subcritical behaviour in dynamos in line with previous studies. We explore the action of Lorentz force in a rotating dynamo which gives rise to a strong preference for dipolar modes over quadrupolar modes, and also makes subcritical behaviour more likely to occur. The coherent structures that arise in rapidly rotating convection are affected by the magnetic field in ways which strongly increase their helicity, particularly if the magnetic field is dipolar. As helicity enhances dynamo action, an existing magnetic field can hold itself up, which leads to subcritical behaviour in the dynamo. We investigate this mechanism by means of the asymptotic small Ekman number theory of rapidly rotating magnetoconvection, and compare our results with fully nonlinear dynamo simulations. There are also other mechanisms which can promote subcritical behaviour. When Reynolds stresses are significant, zonal flows can lower the helicity and disrupt the onset of dynamo action, but an established dipole field can suppress the zonal flow, and hence boost the helicity. Subcriticality means that a slow gradual reduction in Rayleigh number can lead to a catastrophic collapse of the dynamo once a critical Rayleigh number is reached. While there is little evidence that the Earth is currently in a subcritical regime, this may have implications for the long-term evolution of the geodynamo.

JFM classification

MHD and Electrohydrodynamics: Dynamo theory Geophysical and Geological Flows: Geodynamo
Type
Papers
Information
Journal of Fluid Mechanics , Volume 688 , 10 December 2011 , pp. 5 - 30
Copyright
Copyright © Cambridge University Press 2011

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