A self-consistent convection driven geodynamo model, using a mean field approximation

Abstract

The magnetic fields generated by thermal convection in a rapidly rotating fluid spherical shell are studied. The shell is sandwiched between a finitely conducting solid inner core and a non-conducting mantle. As the Rayleigh number is increased, the convective motion becomes stronger; when the magnetic Reynolds number becomes larger than a few hundred, dynamo action onsets, and a magnetic field with both axisymmetric and nonaxisymmetric components develops. The magnetic fields generated are generally of the same order of magnitude as the geomagnetic field, and the outer core fluid velocity is consistent with the values deduced from secular variation observations. A mean field approximation is used in which the dynamics of one non-axisymmetric convective mode (the m = 2 mode being most frequently used) and the associated axisymmetric components are followed. This scheme involves significantly less computation than a fully three-dimensional code, but does not require an arbitrary α-effect to be imposed. Although the Roberts number, q, the ratio of thermal to magnetic diffusion, is small in the Earth, we find that dynamo action is most easily obtained at larger values of q. The Ekman number in our calculations has been taken in the range O(10 −3)- O(10 −4), which, although small, is larger than the appropriate value for the Earth's core. At q = 10 we find solutions at Rayleigh numbers close to critical; two such runs are presented, one corresponding to a weak field dynamo, another to a strong field dynamo; the solution found depends on the initial conditions. At q = 1, the solutions have a complex spatial and temporal structure, with few persistent large-scale features, and our solutions reverse more frequently than the geodynamo. The final run presented has an imposed stable region near the core-mantle boundary. This solution has a weaker non-axisymmetric field, which fits better with the observed geomagnetic field than the solution without the stable layer.