Journal of Conference Abstracts

Numerical Modelling of the Geodynamo: Taylor States and Ekman States

Jeremy Bloxham (bloxham@geophysics.harvard.edu)

Harvard University, 20 Oxford Street, Cambridge, MA 02138, U.S.A.

The last few years have witnessed the development of several dynamically self-consistent numerical models of the geodynamo, some of which have achieved a reasonable, or at least encouraging, agreement with observations of the Earth's magnetic field. Recently, though, it has been demonstrated that two of these models, the Glatzmaier-Roberts and Kuang-Bloxham models, operate in a quite dissimilar fashion, even though they both result in a predominantly dipolar magnetic field at the core surface.

The different modes of dynamo action exhibited by these models result from the manner in which viscous effects are treated: in the Glatzmaier-Roberts model no-slip boundary conditions are applied at the rigid boundaries while in the Kuang-Bloxham model, in an attempt to alleviate computational considerations that restrict such models to values of the Ekman number that are far larger than that which is appropriate for the Earth's core, viscous stress-free boundary conditions are applied.

Several important questions arise. Most critical is the relationship between these two regimes of dynamo action and the dynamical balance that is believed to exist in the Earth's core. In the Earth's core it is widely believed, and there is some observational evidence to support this, that the dynamo is close to a Taylor state with small deviations from that magnetostrophic balance offset by inertia. In the Taylor state viscous effects, as measured by the Ekman number, are largely unimportant.

We examine this issue by performing a series of numerical experiments in which we operate our dynamo model in the Glatzmaier-Roberts regime (by applying no-slip boundary conditions) and in which we vary the Ekman number. We find a power-law scaling between the magnetic field strength and the Ekman number, with B~ E^1/n where n is roughly 3. This is characteristic more of an Ekman state than a Taylor state. Ekman state dynamos are of little relevance to the geodynamo.

As the Ekman number is descreased further, we see a transition to weak-field solutions. Strong-field solutions should then also be present, though locating the strong-field branch then becomes a very expensive undertaking. Ultimately we hope to address the extent to which the original Kuang-Bloxham dynamo with viscous stress-free boundary conditions represents the asymptotic limit of small Ekman number in calculations with no-slip boundary conditions.