Kinematic dynamos in cylindrical geometry

In order to understand the results of recent dynamo experiments, the behavior of kinematic dynamos in cylindrical geometries is analyzed. Simulations are performed applying a hybrid finite volume/boundary element method that allows a stringent treatment of insulating boundary conditions.

A suitable prescribed velocity field, either analytic or -- more realistic -- from measurement data from water experiments, leads to dynamo action, and a strong influence of boundary conditions and additional (stagnant) fluid layers around the active domain is observed.

An additional source term for dynamo action exists in case of a spatially varying conductivity distribution. A very simple set-up -- serving as a proof of concept -- is given by a steady axial flow in an infinite cylinder with inhomogenous container walls. Such a configuration is sufficient for dynamo action, however, the critical Reynolds number might be too large for the realisation in a simple laboratory-sized experiment.

Similiar effects appear in case of permeability inhomogenities, where increased gradients might also lead to a significant reduction of the critical Reynolds number.