Is the geodynamo process intrinsically unstable?

Recent palaeomagnetic studies suggest that excursions of the geomagnetic ¢eld, during which the intensity drops suddenly by a factor of 5^10 and the local direction changes dramatically, are more common than previously expected. The `normal' state of the geomagnetic ¢eld, dominated by an axial dipole, seems to be interrupted every 30^100 kyr; it may not therefore be as stable as we thought. We have investigated a possible mechanism for the instability of the geodynamo by calculating the critical Rayleigh number (Rc) for the onset of convection in a rotating spherical shell permeated by an imposed magnetic ¢eld with both toroidal and poloidal components. We have found Rc to be a very sensitive function of the poloidal ¢eld at the very small Ekman number pertaining to the core. The magnetic Reynolds number, and therefore the dynamo action, is equally sensitive to the applied ¢eld because of its dependence on the di¡erence between the Rayleigh number and its critical value. This explains why numerical dynamo simulations at small Ekman number fail when similar magnetoconvection calculations succeed: the £uctuating magnetic ¢eld of the dynamo leads to rapid swings in convection strength that cannot be resolved numerically. The geodynamo may be unstable for the same reason, with the strength of convection varying wildly in response to the inevitable small changes in magnetic ¢eld. Frequent geomagnetic excursions may therefore be a manifestation of the instability arising from the core's very weak viscosity and the controlling e¡ects of the Earth's rotation.