A criterion for the existence of polar vortices in the Earth’s core

Observations of the Earth’s magnetic field indicate that there are anticyclonic polar vortices in the core. In the presence of the self-generated magnetic field, the polar azimuthal flow is believed to be produced by one or more coherent upwellings within the tangent cylinder, offset from the rotation axis. In this study, convection within the tangent cylinder in rapidly rotating dynamos is understood through the analysis of forced magnetic waves in an unstably stratified fluid. In the dipole-dominated dynamo regime, the isolated upwellings within the tangent cylinder are produced by the localized excitation of slow Magnetic-Archimedean-Coriolis (MAC) waves. If the forcing is so strong as to cause the collapse of the axial dipole, the convection takes the form of an ensemble of plumes supported entirely by fast waves whose frequency is of the same order as that of linear inertial waves. The resulting weak polar circulation is comparable to that in nonmagnetic convection. The observed peak azimuthal motions of 0.6 to 0.9° yr^-1 are obtained only in the dipolar dynamo regime, where the Rayleigh number must be of ~10³ times the Rayleigh number for the onset of nonmagnetic convection.