Numerical simulation of a spherical dynamo excited by a flow of von Kármán type

Abstract

In a celebrated recent experiment, Monchaux, et al. (Phys. Rev. Lett. 2007, 98, 044502) created a self-excited dynamo in a cylindrical container of liquid sodium by a turbulent flow created by counter-rotating impellers at the plane ends of the container. A strange feature of the experiment was its failure to generate magnetic field when the impellers were made of stainless steel; success required the impellers to be made of soft iron. The results reported here were generated by numerical simulations of an idealization of the experiment. The container is a sphere and the impellers are replaced by a differential zonal motion of its surface, the northern and southern hemispheres turning about the symmetry axis in opposite senses, the whole system being contained in a thin shell with which it is in perfect electrical contact. This shell has generally a finite electrical conductance and a magnetic permeability that can greatly exceed that of the fluid. The electrodynamic effect of the shell is represented by a thin-wall boundary condition, similar but not identical to that used in MHD duct flow theory. Eleven cases were considered, in four of which the surface shell is an electrical insulator; in the others it is made of a conducting material which, like soft iron, might have a large permeability. In eight cases, a seed field decays away but in three it is amplified and becomes a turbulent self-excited dynamo. Through four cases of the same surface motion and shell permeability, it is inferred that an increase in the shell conductance assists the regeneration of magnetic field. It is also shown that enhancing the shell permeability assists the field creation.