Magnetohydrodynamics in Rapidly Rotating spherical Systems

Recent developments in the study of buoyancy-driven convection, magnetoconvection, and convection-driven dynamos in rapidly rotating spherical systems, with application to the fluid parts of the metallic cores of the Earth and other planets and satellites, are reviewed. While the fluid motions driven by convection generate and sustain magnetic fields by magnetohydrodynamic dynamo processes, the pattern and strength of the convective motions that control dynamo action are critically influenced by the combined and inseparable effects of rotation, magnetic fields, and spherical geometry. Emphasis is placed on the key dynamic feature of rotating spherical magnetohydrodynamics—the interaction between the Coriolis and Lorentz forces and the resulting effect on convection and magnetohydrodynamic processes. It is shown that the small value of the Ekman number, a result of rapid rotation and small viscosity in the fluid parts of planetary cores, causes severe difficulties in modeling planetary dynamos. There exist huge disparities, as a direct consequence of a small Ekman number, in the spatial, temporal, and amplitude scales of a convection-driven dynamo. The use of hyperviscosity removes these difficulties, but at the same time it alters the key dynamics in a fundamental and undesirable way. A convection-driven dynamo solution in rotating spherical systems at a sufficiently small Ekman number that is dynamically relevant to planetary fluid cores is yet to be achieved and remains a great challenge.