Electromagnetic induction in non-uniform domains

Kinematic simulations of the induction equation are carried out for different setups suitable for the von-Karman-Sodium (VKS) dynamo experiment. The material properties of the flow driving impellers are modeled by means of high-conducting and high-permeability disks in a cylindrical volume filled with a conducting fluid. Two entirely different numerical codes are mutually validated by showing quantitative agreement on Ohmic decay and kinematic dynamo problems using various configurations and physical parameters. Field geometry and growth rates are strongly modified by the material properties of the disks even if the disks are thin. In contrast the influence of external boundary conditions remains small. Utilizing a VKS like mean fluid flow and high-permeability disks yield a reduction of the critical magnetic Reynolds number Rmc for the onset of dynamo action of the simplest non-axisymmetric field mode. However, this threshold reduction is not sufficient to fully explain the VKS experiment. We show that this reduction of Rmc is influenced by small variations in the flow configuration so that the observed reduction may be changed with respect to small modifications of setup and properties of turbulence.