Theory and Modeling of Planetary Dynamos

Abstract

Numerical dynamo models are increasingly successful in modeling many features of the geomagnetic field. Moreover, they have proven to be a useful tool for understanding how the observations connect to the dynamo mechanism. More recently, dynamo simulations have also ventured to explain the surprising diversity of planetary fields found in our solar system. Here, we describe the underlying model equations, concentrating on the Boussinesq approximations, briefly discuss the numerical methods, and give an overview of existing model variations. We explain how the solutions depend on the model parameters and introduce the primary dynamo regimes. Of particular interest is the dependence on the Ekman number which is many orders of magnitude too large in the models for numerical reasons. We show that a minor change in the solution seems to happen at E = 3×10 −6 whose significance, however, needs to be explored in the future. We also review three topics that have been a focus of recent research: field reversal mechanisms, torsional oscillations, and the influence of Earth's thermal mantle structure on the dynamo. Finally we discuss the possibility of tidally or precession driven planetary dynamos.

Hydromagnetic dynamos in rotating spherical fluid shells in dependence on the Prandtl number, density stratification and electromagnetic boundary conditions

“…Numerical modelling of self-consistent dynamos has made noticeable progress in the last years due to the progress in computer technology. The results of numerical simulations are in very good agreement with the observations of the recent geomagnetic field and with paleomagnetic research (Roberts and Glatzmaier, 2000;Glatzmaier, 2005;Fearn, 2007;Christensen and Wicht, 2007;Wicht and Tilgner, 2010;Sakuraba and Roberts, 2009). 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 constitute the driving mechanism of dynamos, i.e.…”

Iron snow dynamo models for Ganymede

“…by tidal or librational effects (Wicht and Tilgner, 2010), aside, flow in a metallic planetary core can be driven by thermal convection or by compositional convection. A condition for thermal convection to occur is that the heat flow out of the core is larger than the heat transported by conduction along an adiabatic temperature gradient.…”

Three-dimensional quasi-geostrophic convection in the rotating cylindrical annulus with steeply sloping endwalls

“…Such models provide a means of reaching realistic fluid properties and flow parameters that are currently out of reach to current dynamo models (cf. Wicht & Tilgner 2010). The 3D-QGCM presented here can be extended easily to include more complex physics including spherical gravity and anelasticity (e.g.…”