Numerical modelling of the geodynamo: a systematic parameter study

We analyse similar to 50 3-D numerical calculations of hydrodynamic dynamos driven by convection in a spherical shell. We examine rigid and stress-free boundaries, with Prandtl number 1, magnetic Prandtl numbers in the range 0.5-5, Ekman numbers E = 10(-3)-10(-4) and Rayleigh numbers to 15 times critical. No parametrizations such as hyperviscosities are used. Successful dynamos are compared with non-magnetic convection solutions. Results for various spectral truncations suggest that the calculations are well resolved when the kinetic and magnetic energy drops by more than two orders of magnitude from the spectral peak to the cut-off, although the basic features are still captured at lower resolution. With few exceptions we obtain dipole-dominated magnetic fields. The dynamos operate in the strong-field regime where Lorentz and Coriolis forces are of similar order. The critical magnetic Reynolds number for self-sustained dynamos is of order Rm = 50. However, we also find that the field can die away when Rm is too large. The minimum magnetic Prandtl number at which we find dynamo action depends on the Ekman number to the 3/4 power. Dynamos at E = 10(-3) are subcritical whereas those at E = 10(-4) are generally supercritical. The presence of the magnetic field tends to break the equatorial symmetry of the flow and favours convection inside the inner core tangent cylinder. With stress-free boundaries, dynamo action suppresses the axisymmetric azimuthal wind that dominates in non-magnetic convection. The field morphology is broadly similar for both kinds of boundary conditions. When low-pass filtered, several models exhibit field structures that resemble the geomagnetic field at the core-mantle boundary to a surprising degree.