Convection–driven geodynamo models

Abstract

There has been signi cant progress in the development of numerical geodynamo models over the last ve years. Advances in computer technology have made it possible to perform three-dimensional simulations, with thermal or compositional convection as the driving mechanism. These numerical simulations give reasonable results for the morphology and strength of the eld at the core{mantle boundary, and the models are also capable of giving reversals and excursions which can be compared with palaeomagnetic observations; they also predict di¬erential rotation between the inner core and the mantle.However, there are still a number of fundamental problems associated with the simulations, which are proving hard to overcome. Despite the advances in computing power, the models are still expensive and take a long time to run. This problem may diminish as faster machines become available, and new numerical methods exploit parallelization e¬ectively, but currently there are no practical schemes available which work at low Ekman number.Even with turbulent values of the di¬usivities (and the question of whether isotropic di¬usivities are appropriate is still unresolved), the appropriate dynamical regime has not yet been reached. In consequence, modelling assumptions about the nature of the ®ow near the boundaries have to be made, and di¬erent choices can have profound e¬ects on the dynamics. The nature of large-scale magnetoconvection at small E is still not well understood, and until we have more understanding of this issue, it will be di¯cult to have a great deal of con dence in the predictions of the numerical models.

Reversals in the six-jet Geodynamo model

“…2 is 5 × 10 −4 m/s. This agrees well with the known estimates of the actual velocity of convection ∼ 10 −4 m/s [1]. The characteristic value of the field in the model 5 × 10 −4 T is also in good agreement with the extrapolation of the real magnitude of the geomagnetic field at the boundary of the outer core [9].…”

“…The process of formation of magnetic fields of planets and stars is successfully explained by the theory of hydromagnetic dynamo [1,2]. The existing models reproduce MHD flows on a small-scale spatial grid at relatively small timescales (∼ 50 kyr), or make it possible to calculate only the long-evolution large spatial structures.…”

Theory and Modeling of Planetary Dynamos

“…However, the difference seems to vanish at larger Rayleigh numbers and smaller Ekman numbers. More research is required to elucidate the true saturation mechanism which may actually be quite subtle (Jones 2000).…”

“…Several publications provide extensive overviews of the different aspects in numerical dynamo simulations (Braginsky and Roberts 1995;Jones 2000Jones , 2007Glatzmaier 2002) and discuss their success in modeling the geomagnetic field (Kono and Roberts 2002;Christensen and Wicht 2007). Here, we concentrate on more recent developments that mainly concern the geodynamo.…”

Convection in rotating non-uniformly stratified spherical fluid shells in dependence on Ekman and Prandtl numbers

“…Convection (magnetoconvection) constitutes the driving mechanism of hydromagnetic processes leading to magnetic field generation [15]. Buoyancy, the fundamental source of convection or magnetoconvection [11], results from the complicated processes going on in the Earth's and planetary fluid interiors, e.g., a chemical homogenisation, gravitational differentiation, solidification processes acting on the inner core boundary (e.g., the convection in the mushy layer due to the mentioned solidification processes, see [9]), etc. Consequently, the outer liquid Earth's core and the liquid interiors of Giant planets are nonuniformly stratified (this means density stratification, see [8,24]).…”