Dynamically consistent spherical mean-field dynamo models

Spherical mean-field dynamo models are considered which involve in part the interaction between the magnetic field and the motion of the electrically conducting fluid. Whereas the influence of the magnetic field on the small-scale motions responsible for the α-effect is ignored, the effect of the Lorentz force due to the mean magnetic field on the mean motion is taken into account. The evolution of the mean magnetic field and the mean motion is studied numerically for two different boundary conditions for this motion, viz. the no-slip condition and the condition of a stress-free surface. Several steady states have been found with different symmetries with respect to the equatorial plane and the rotation axis of the fluid body. The stability of these states clearly differs for the two boundary conditions. In one case an evolution to an axisymmetric state is preferred; in the other case to an non-axisymmetric one. In addition to the steady solutions with simple symmetries an oscillatory mixed-parity solution has also been found.