Reversals and the turbulent alpha-effect in kinematic simulations of natural and experimental dynamos

From paleomagnetic observations, numerical simulations and -- meanwhile -- also experiments, it is evident that reversing dynamos are a quite common phenomenon. An easy access to the examination of reversing dynamos is provided by simplifying mean field simulations where the induction effects of helical small scale turbulence are parametrized by the so called α-effect.

In a geodynamo-like α²-model reversing solutions are obtained only for a highly restricted class of radial α-profiles which are characterized by a proximity of oscillating and non-oscillating state. The required properties of the α-effect, indeed, have been found from local simulations of rotating magnetoconvection in a Cartesian box (Giesecke et al. 2005, PEPI 152, 90-102). Essential properties of the field reversals can be assigned to the behavior of so called exceptional points in the spectrum of the dynamo-operator where two different non-oscillatory field eigenmodes merge and continue as one oscillatory eigenmode (Stefani et al. 2005, PRL, 94, 184506). The connection between oscillating solutions and irregular occurring reversals arises from fluctuations of the α-effect, which causes a sporadic switching from steady to the oscillatory regime and vice versa. In this picture a reversal is an inevitable consequence of the behavior of the instantanous growthrate in conjuction with fluctuations of the driving source.

Recent results of the French von-Kármán-Sodium (VKS) dynamo offer a possibility for detailed investigations of reversing magnetic fields. In the VKS experiment a turbulent flow of liquid sodium is driven by two counter rotating soft iron impellers located close to the endplates of a cylindrical vessel. The geometric structure of the observed magnetic field is dominated by an axisymmetric dipole that exhibits regular and irregular reversals if the impellers rotate with different frequencies. Recent simulations show that the induction process is essentially determined by the material properties of the flow driving impellers (high permeability) because of internal boundary conditions for the magnetic field on the interface between fluid and impeller (Giesecke et al. 2010, PRL 104, 044503). However, only the combined interaction of soft iron disks and a comparatively small α-effect allows to explain the dominating axisymmetric field. Contributions of dipole and quadrupole type fields deduced from the equatorial symmetry show nearly the same growth rate supporting the reversal model presented by Pétrélis & Fauve (2009, PRL 102, 144503) that is based on the coupling between these two modes.