The influence of boundary region heterogeneities on the geodynamo

Abstract

We investigate the effect of two deviations from the standard picture of rotating, buoyancy-driven convection on a model of the geodynamo, motivated by conditions which may pertain near the core-mantle boundary in the Earth. First, the effect of a thin stably stratified layer in the vicinity of the outer boundary of the fluid, such as has been hypothesised for the convective state of the core, is considered. Second, an inhomogeneous boundary condition is imposed, motivated by the likelihood of coupling from the mantle significantly affecting convection in the core. To model the generation of magnetic fields in a rapidly rotating, convecting spherical shell, a self-consistent mean-field model is adopted. Only a single non-axisymmetric mode is considered, but the mutual interaction between this mode and the axisymmetric mean-field is entirely incorporated. The stably stratified layer has the effect of stabilising the oscillatory or chaotic magnetic fields obtained in a globally unstable system, creating a magnetic field pattern which co-rotates with the drifting convective rolls. The further imposition of a heterogeneous boundary condition can then serve to ‘lock’ the flow, and also the magnetic flux, at longitudes determined by the forcing employed. For small imposed heterogeneities, the locking can only be defined via a time-average. For slightly larger heterogeneities, the locking can be total, with flow and field completely frozen. This behaviour can to some extent be understood with reference to a simple amplitude equation analogue. The total range of behaviour exhibited by the dynamo system is more complex however. Yet stronger imposed heterogeneities can lead to the magnetic field significantly affecting the boundary-driven flow, and the stationary solution being lost, although locking in the time-averaged sense still prevails. Furthermore, solutions at specific model parameters are non-unique, being dependent upon the initial state employed in the calculations. The basic mechanism is clear, however, and allows solutions similar to the observed geomagnetic field to be obtained. Further work may take advantage of these possible clues as to the mechanisms operating within the geodynamo, whilst employing parameter values closer to those anticipated in the Earth than we have been able to attain here.