Table of contents

As a consequence of the smallness of the electronic fine structure constant, the characteristic time scale for the free diffusive decay of a magnetic field in a planetary core is much less than the age of the Solar System, but the characteristic time scale for thermal diffusion is greater than the age of the Solar System. Consequently, primordial fields and permanent magnetism are small and the only means of providing a substantial planetary magnetic field is the dynamo process. This requires a large region which is fluid, electrically conducting and maintained in a non-uniform motion that includes a substantial RMS vertical component. The attributes of fluidity and conductivity are readily provided in the deep interiors of all planets and most satellites, either in the form of an Fe alloy with a low eutectic temperature (e.g. Fe-S-O in terrestrial bodies and satellites) or by the occupation of conduction states in fluid hydrogen or 'ice' (H₂O-NH₃-CH₄) in giant planets. It is argued that planetary dynamos are almost certainly maintained by convection (compositional and/or thermal).

The action of turbulence on a passive convected scalar field (e.g. temperature) or vector field (e.g. the magnetic field in an electrically conducting fluid) is reviewed, with particular attention paid to anomalous effects that can arise through the influence of Coriolis forces in a rotating system on the statistics of the turbulence. The simplest such effect (which corresponds to a breaking of the Onsager symmetry relations) is a 'skew-diffusion' effect, i.e. the appearance of a component of turbulent heat flux perpendicular to the local mean temperature gradient. The famous alpha effect of magnetohydrodynamic dynamo theory is also in this category, as is the more subtle Radler effect (the appearance of a mean electromotive force perpendicular to the mean current in a plasma). These effects are all associated with the helicity of a turbulent flow, i.e. the correlation between the velocity field u(x,t) and the vorticity field omega (x,t)=curl u.