Analysis of the variability of the axial dipole moment of a numerical geodynamo model

We have analysed the time evolution of the axial dipole moments (ADMs) from three numerical geodynamo models by relating it to the Fokker–Planck equation governing the systematic and random ADM motion. We have determined the effective growth rate of the ADM and the diffusion coefficient D characterising its random fluctuations. We find that the numerical ADM data exhibit a nonlinear quenching that is not significantly different from that of the Sint-2000 data. The quenching is only partly due to a reduction of the r.m.s. convective flow speed with increasing ADM. Our results suggest that in these numerical models similar mechanisms may be at work as in the earth’s core, and that the results of Brendel et al. [Brendel, K., Kuipers, J., Barkema, G.T., Hoyng, P., 2007. An analysis of the fluctuations of the geomagnetic dipole. Phys. Earth Planet. Inter. 162, 249–255] are unlikely to be an artifact caused by the restricted length of the dataset. They also suggest that the dynamics of the ADM is that of a Brownian particle (i.e. driven by additive noise) in a bistable potential, and we illustrate some consequences of this idea.