Approaching the Geodynamo Through an Inviscid Convective Dynamo Model

Abstract:

The Earth's magnetic field is believed to be generated in the Earth’s fluid metallic outer core, through a process termed ’self-excited dynamo action’. Thermal and compositional convection motions, which induce an electrical current and an associated magnetic field, arrange themselves in such a way that this magnetic field is sustained. Although first proposed by Larmor in 1919, the details of this mechanism still remain an outstanding problem. Direct numerical simulation (DNS) has proven to be successful over the last twenty years, leading to a comprehensive classification of dynamos in which viscosity is significantly present. One key feature of the geodynamo, which turns out to be the critical constraint on numerical modelling, is rapid rotation. Dominance of the Coriolis force over viscous and inertial effects makes it extremely difficult for DNS to reach Earth-like parameters. Taylor (1963) developed a model in which both inertial and viscous effects are neglected. In such a case, the momentum equation represents a force balance between Coriolis, pressure, buoyancy and Lorentz forces. A modification of such a model, presaged by Taylor, is to reintroduce the inertial term governing the geostrophic flow. Both models have been studied and realised in the axisymmetric mean-field dynamo context by Wu and Roberts (2015), Li et al. (2018) and Roberts and Wu (2018). In this study, for the first time we find a convectively-driven three dimensional inviscid dynamo in a sphere with Taylor's modified model. For the thermal forcing (measured by the Rayleigh number) considered here, a chaotic solution is obtained, which is dominated by a non-reversing dipolar component. Torsional waves are excited and propagate both inwards and outwards through the geostrophic cylinders. DNS with stress-free boundaries or rigid boundaries that are made for comparison at similar parameters using relatively low Ekman numbers do not exhibit dipolar field structure. The result suggests that the inviscid model favours more dipolar solutions compared to viscous ones, and may indicate that most of the known viscous dynamos are not yet in a regime of the geodynamo.