Is the geodynamo process intrinsically unstable?

Abstract

S U M M A RYRecent 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 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.

The Blake geomagnetic excursion recorded in a radiometrically dated speleothem

“…It is intriguing that the duration of each reversed episode is within the range observed for single excur sions (1.6 kyr for B2 and 2.3 kyr for El). Laj and Channell (2007) consider that the instability associated to the Blake excursion may be explained by the observation that the critical Reynolds number for the onset of core convection is very sensitive to the poloidal field, and the strength of the core convection varies widely in response to changes in magnetic field strength particularly during intensity minima (Zhan and Gubbins, 2000). The origin of excur sions remains an open question and accurate determination of their duration can be a key to constrain the geomagnetic models.…”

Convection–driven geodynamo models

“…The problem with this scenario is that the magnetic eld needs to be su¯ciently strong everywhere and at all times to sustain convection on a large length-scale (Zhang & Gubbins 2000). If, due to ®uctuations, the eld becomes small over a signi cant domain for a signi cant period (e.g.…”

Scale disparities and magnetohydrodynamics in the Earth's core

“…It should be noted that the fully nonlinear magnetoconvection solution with both the toroidal and poloidal eld is reported here for the rst time, but the linear stability calculations have been described in Zhang & Gubbins (2000). A more detailed analysis of the nonlinear problem will be reported in a future paper.…”