Scale disparities and magnetohydrodynamics in the Earth’s core

Fluid motions driven by convection in the Earth’s fluid core sustain geomagnetic ­ fields by magnetohydrodynamic dynamo processes. The dynamics of the core is critically influenced by the combined effects of rotation and magnetic ­ fields. This paper attempts to illustrate the scale-related difficulties in modelling a convection-driven geodynamo by studying both linear and nonlinear convection in the presence of imposed toroidal and poloidal ­ fields. We show that there exist three extremely large disparities, as a direct consequence of small viscosity and rapid rotation of the Earth’s fluid core, in the spatial, temporal and amplitude scales of a convection-driven geodynamo. We also show that the structure and strength of convective motions, and, hence, the relevant dynamo action, are extremely sensitive to the intricate dynamical balance between the viscous, Coriolis and Lorentz forces; similarly, the structure and strength of the magnetic field generated by the dynamo process can depend very sensitively on the fluid flow. We suggest, therefore, that the zero Ekman number limit is strongly singular and that a stable convection-driven strong-­field geodynamo satisfying Taylor’s constraint may not exist. Instead, the geodynamo may vacillate between a strong ­field state, as at present, and a weak ­ field state, which is also unstable because it fails to convect sufficient heat.