Chaotic dynamics of the magnetic field generated by dynamo action in a turbulent flow

We present models related to the results of a recent experiment (the 'VKS experiment') showing the generation of a magnetic field by a fully turbulent flow of liquid sodium. We first discuss the geometry of the mean magnetic field when the two coaxial impellers driving the flow counter-rotate at the same frequency. We then show how we expect this geometry to be modified when the impellers rotate at different frequencies. We also show that, in the latter case, dynamical regimes of the magnetic field can be easily understood from the interaction of modes with dipolar (respectively quadrupolar) symmetry. In particular, this interaction generates magnetic field reversals that have been observed in the experiment and display a hierarchy of timescales similar to the Earth's magnetic field: the duration of the steady phases is widely distributed, but is always much longer than the time needed to switch polarity. In addition to reversals, several other large scale features of the generated magnetic field are obtained when varying the governing parameters of the flow. These results are also understood in the framework of the same model.