Convection driven geodynamo models of varying Ekman number

Abstract

We investigate the dynamo action arising from convection in a rapidly-rotating spherical shell. A single mode of the non-axisymmetric field is solved for, in addition to the axi-symmetric (mean) field. This allows dynamo action to be obtained without any imposed parameterisation, yet results in a system tractable enough that a range of physical regimes can be investigated. We describe the different types of dynamo obtained for varying Ekman and Roberts numbers. For the smaller values of these parameters, hyper-diffusivities have been used to model the effects of small lengthscale turbulent diffusion. At relatively high Ekman numbers (c. 10-3) dynamo action is obtained for moderately supercritical convective flows, with the flow in the form of travelling-wave convective rolls. At lower (hyperdiffusive) Ekman numbers, magnetic field maintenance occurs only for strongly supercritical flows. The resultant dynamos are temporally chaotic and dominated by strong fields and flows in the vicinity of the inner core, resembling the fully three-dimensional solutions of Glatzmaier and Roberts (1995b, 1996a). The inner core plays a critical role in these solutions, and rotates progradely at of order 1° per year. Calculations are conducted with ‘dipolar’ equatorial symmetry imposed and with no imposed symmetry. The imposed symmetry constraint proves an unphysical restriction for all our solutions. At lower Ekman numbers, the equatorially symmetric magnetic field is only intermittently significant; fluctuations in this component remain a plausible ‘trigger’ for reversals of the dominant dipole field, however, and so potentially important for the geodynamo. Taylor torque ‘integrals are calculated to quantify the adjustment of our solutions to the low viscosity regime. Our low Ekman number solutions satisfy the Taylor constraint appropriate to this regime more poorly than those at high Ekman number, however. Here the Lorentz torque on coaxial cylinders is balanced by the viscous torque associated with the hyperdiffusively-affected short wavelength velocities. Thus these solutions also remain viscously controlled, and might be expected to depend somewhat on the form of hyperviscosity assumed. At neither high nor low Ekman numbers does removing the imposed symmetry constraint reliably assist towards satisfying Taylor's constraint.