Numerical models of the geodynamo and observational constraints

Abstract

[1]0 Abstract: The past few years have seen the emergence of a large number of numerical simulations of the geodynamo. In parallel, both new and old geomagnetic, archeomagnetic, and paleomagnetic observations have been interpreted as actual geomagnetic features and used as constraints for dynamo models. Naturally, model predictions should be tested against actual characteristics of the geomagnetic field. Despite huge differences (sometimes in excess of a billion) between the values of parameters used in the simulations and those estimated for the Earth, it is intriguing that many available simulations succeed in producing largely axial dipolar magnetic fields with weaker nondipolar structures, in agreement with the first-order characteristics of the geomagnetic field. Yet, when considering finer characteristics, there are significant differences, and failures to actually produce a number of fundamental characteristic features. In this presentation, we first review numerical results obtained to date, then we attempt to summarize which field characteristics derived from observational data sets can be considered robust. On the basis of simple criteria used to evaluate the degree of confidence that can be placed in each datum, we sort presumably characteristic geomagnetic features into three categories (robust, controversial, and unlikely). We conclude that numerical models should be illustrated with a number of key``predictions,'' averaged over at least 10 dipole diffusion times. These predictions should be tested against the subset of robust observations only. Controversial observations should await additional confirmation.

Correlation of Earth’s magnetic field with lower mantle thermal and seismic structure

“…There is further evidence to suggest that lower mantle variations affect the Earth's dynamo: the frequency of polarity reversals changes on the very long timescale of mantle convection (Merrill & McElhinny, 1996), the poles follow preferred paths during polarity A c c e p t e d M a n u s c r i p t transition (Laj et al, 1991;Love, 2000), and secular variation in the Pacific is low (Doell & Cox, 1972;Coe et al, 1978). These correlations are controversial (Dormy et al, 2000) but a single theory can explain all the above features. Several geodynamo computer simulations have incorporated lower mantle seismic shear wave velocity as a proxy for heat flux out of the core (Glatzmaier et al, 1999;Bloxham, 2000a,b;Olson & Christensen, 2002;Christensen & Olson, 2003;Aubert et al, 2007) but the generated fields have fluctuated too rapidly in time to allow a straightforward correlation with the observed geomagnetic field.…”

Bistability and hysteresis of dipolar dynamos generated by turbulent convection in rotating spherical shells

“…The dynamo effect of turbulent convection in rotating spherical fluid shells has received much attention in recent years [3,4] because it is the basic model for the generation of the magnetic fields of the Earth and other planets. Many numerical studies following [5,6] have attempted a direct comparison with geomagnetic observations and have been remarkably successful in reproducing some of the main properties of the geomagnetic field [7,8] while others have focused on more systematic explorations of the computationally accessible parameter space e.g. [9][10][11][12][13].…”

“…In addition to d, we use the time d 2 /ν, the temperature ν 2 /γαd 4 and the magnetic flux density ν(µ̺) 1/2 /d as scales for the dimensionless description of the problem where ν denotes the kinematic viscosity of the fluid, κ its thermal diffusivity, ̺ its density and µ its magnetic permeability. In common with most other simulations of Earth and planetary dynamos [4,7], we assume the Boussinesq approximation implying a constant density ̺ except in the gravity term where its temperature dependence is taken into account with α ≡ −( d̺/ dT )/̺ =const. The equations of motion for the velocity vector u, the heat equation for the deviation Θ from the static temperature distribution, and the equation of induction for the magnetic flux density B are then given by…”

Mechanisms for magnetic field reversals

“…Since 1995 (Glatzmaier & Roberts 1995), a lot of three-dimensional numerical simulations of the MHD equations in a rotating sphere have been able to simulate a self-consistent magnetic field that displays reversals (see the reviews by Dormy et al (2000) and Roberts & Galtzmaier (2000)). However, it has been emphasized that most relevant dimensionless parameters that can be achieved in direct simulations are orders of magnitude away from their value in the Earth's core or laboratory experiments.…”