THE TIME-AVERAGED MAGNETIC FIELD IN NUMERICAL DYNAMOS WITH NON-UNIFORM BOUNDARY HEAT FLOW

Abstract

The time-averaged geomagnetic field on the core-mantle boundary is interpreted using numerical models of fluid dynamos driven by non-uniform heat flow. Dynamo calculations are made at Prandtl number $Pr = 1$, magnetic Prandtl numbers $Pm = 1-2$, Ekman numbers $E = 3 × 10-4 -3 × 10-5 $ and Rayleigh numbers 10-30 times the critical value for different patterns of heat flow on the outer boundary of a rotating, electrically conducting spherical shell. The results are averaged over several magnetic diffusion times to delineate the steady-state magnetic field and fluid motion. When the boundary heat flow is uniform the time-averaged flow approaches axisymmetry and the magnetic field is mostly a geocentric axial dipole (GAD). The largest departure from GAD in this case is the octupole field component. When the amplitude of the boundary heat flow heterogeneity exceeds the average heat flow, the dynamos usually fail. Lesser amounts of boundary heterogeneity produce stable dynamos with time-averaged magnetic fields that depend on the form of the boundary heterogeneity. Elevated heat flow in the northern hemisphere produces a time-averaged axial quadrupole magnetic field comparable to the inferred paleomagnetic quadrupole. Azimuthally periodic boundary heat flow produces a time-averaged magnetic field component with the same azimuthal wavenumber, shifted in longitude relative to the heat flow pattern. Anomalously high and anomalously low magnetic flux density correlate with downwellings and upwellings, respectively, in the time-averaged fluid motion. A dynamo with boundary heat flow derived from lower-mantle seismic tomography produces anomalous magnetic flux patches at high latitudes and westward fluid velocity in one hemisphere, generally consistent with the present-day structure of the geodynamo.