Is the geodynamo process intrinsically unstable?

Abstract

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 (R c ) 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 R c 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 dierence 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 eects of the Earth's rotation.