CONVECTION DRIVEN GEODYNAMO MODELS OF VARYING EKMAN NUMBER

We investigate the dynamo action arising from convection in a rapidly- rotating spherical shell. A single mode of the non-axisymmetric held i s solved for, in addition to the axisymmetric (mean) field. This allow s dynamo action to be obtained without any imposed parameterisation, y et results in a system tractable enough that a range of physical regim es can be investigated. We describe the different types of dynamo obta ined for varying Ekman and Roberts numbers. For the smaller values of these parameters, hyperdiffusivities have been used to model the effec ts of small lengthscale turbulent diffusion. At relatively high Ekman numbers (c. 10(-3)) dynamo action is obtained for moderately supercrit ical convective flows, with the flow in the form of travelling-wave co nvective rolls. At lower (hyperdiffusive) Ekman numbers, magnetic fiel d maintenance occurs only for strongly supercritical flows. The result ant dynamos are temporally chaotic and dominated by strong fields and flows in the vicinity of the inner core, resembling the fully three-di mensional solutions of Glatzmaier and Roberts (1995b, 1996a). The inne r core plays a critical role in these solutions, and relates progradel y at of order 1 degrees per year. Calculations are conducted with 'dip olar' equatorial symmetry imposed and with no imposed symmetry. The im posed symmetry constraint proves an unphysical restriction for all our solutions. At lower Ekman numbers, the equatorially symmetric magneti c field is only intermittently significant; fluctuations in this compo nent remain a plausible 'trigger' for reversals of the dominant dipole field, however, and so potentially important for the geodynamo. Taylo r torque integrals are calculated to quantify the adjustment of our so lutions to the low viscosity regime. Our low Ekman number solutions sa tisfy the Taylor constraint appropriate to this regime more poorly tha n those at high Ekman number, however. Here the Lorentz torque on coax ial cylinders is balanced by the viscous torque associated with the hy perdiffusively-affected short wavelength velocities. Thus these soluti ons also remain viscously controlled, and might be expected to depend somewhat on the form of hyperviscosity assumed. At neither high nor lo w Ekman numbers does removing the imposed symmetry constraint reliably assist towards satisfying Taylor's constraint.