Helicity generation and subcritical behaviour in rapidly rotating dynamos

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.