LINEAR MAGNETOCONVECTION IN A ROTATING SPHERICAL-SHELL, INCORPORATINGA FINITELY CONDUCTING INNER-CORE

The problem of the onset of convection in a rotating spherical shell w ith an imposed magnetic field is studied. This problem is relevant to understanding the dynamics of the Earth's outer core. The finite condu ctivity of the inner core is taken into account and no-slip boundary c onditions are assumed at the inner-core and core-mantle boundaries. Th e problem is investigated numerically, using values of the Ekman numbe r down to 10(-6). Models in which the toroidal magnetic field vanishes near the core-mantle boundary, as expected in the Earth, are consider ed. We find the preferred non-axisymmetric wavenumber, in, of modes pr oportional to exp (im phi) as a function of Elsasser number Lambda. We also find that toroidal fields with Lambda greater than or equal to 1 0 are unstable due to magnetic instability even when there is no therm al driving, i.e. at zero Rayleigh number. In the range of Elsasser num ber appropriate to the geodynamo, convective motions in the interior o f the outer core in our model have azimuthal velocities which are only weakly dependent on the coordinate parallel to the rotation axis. We have also compared the fields and fluid velocities arising from our mo del with those deduced from geomagnetic data, to the extent possible i n our very simplified models. We find that solutions with the m = 2 mo de best resemble published maps of the geomagnetic field at the core s urface. Our calculations generally support the hypothesis that large s cale convection is occurring in the Earth's outer core.