A SELF-CONSISTENT CONVECTION DRIVEN GEODYNAMO MODEL, USING A MEAN-FIELD APPROXIMATION

The magnetic fields generated by thermal convection in a rapidly rotat ing fluid spherical shell are studied. The shell is sandwiched between a finitely conducting solid inner core and a non-conducting mantle. A s the Rayleigh number is increased, the convective motion becomes stro nger; when the magnetic Reynolds number becomes larger than a few hund red, dynamo action onsets, and a magnetic field with both axisymmetric and nonaxisymmetric components develops. The magnetic fields generate d are generally of the same order of magnitude as the geomagnetic fiel d, and the outer core fluid velocity is consistent with the values ded uced from secular variation observations. A mean field approximation i s used in which the dynamics of one non-axisymmetric convective mode ( the m = 2 mode being most frequently used) and the associated axisymme tric components are followed. This scheme involves significantly less computation than a fully three-dimensional code, but does not require an arbitrary cu-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 n umbers close to critical; two such runs are presented, one correspondi ng to a weak field dynamo, another to a strong field dynamo; the solut ion found depends on the initial conditions. At q = 1, the solutions h ave a complex spatial and temporal structure, with few persistent larg e-scale features, and our solutions reverse more frequently than the g eodynamo. The final run presented has an imposed stable region near th e core-mantle boundary. This solution has a weaker non-axisymmetric fi eld, which fits better with the observed geomagnetic field than the so lution without the stable layer.