Abstract
This is an attempt to understand better the dynamics of the small-scale compositionally buoyant flow in the Earth's core which may be responsible for the generation of the Earth's magnetic field by dynamo action, by determining the rise law and the flow structures of a buoyant rigid cylinder rising in a rotating electrically conducting fluid in the presence of a large-scale magnetic field. The problem is linearized by assuming small Rossby and magnetic Reynolds numbers, and the Lorentz force is assumed to be larger than the viscous and Coriolis forces. It is found that the rise speed is larger than one would expect from simple scaling arguments. This rapid speed is related to the large-scale flow structures, elongated in the direction of the applied magnetic field, which carry the electric currents associated with the Lorentz force. This elongation serves to weaken the Lorentz force such that the force balance within these structures is magnetostrophic (between Coriolis and Lorentz). The restriction to the case of a rigid cylinder makes this study directly applicable only to the polar regions of the outer core.
