Hydromagnetic αΩ-type dynamos with feedback from large scale motions

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Abstract
Nonlinear axisymmetric mean-field αΩ-type dynamos in spherical shells of conducting incompressible fluid are computed, with differential rotation being generated by the Reynolds stress of anisotropic turbulence (A-effect). The correlation time of the turbulence is assumed to be short compared with the rotation period. In this case the angular velocity tends to be constant on cylindrical surfaces as the Taylor number, Ta, is increased (cf. the Taylor-Proudman theorem). The only magnetic feedback mechanism considered is the Lorentz force of the mean magnetic field acting on the macroscale motions (Malkus-Proctor mechanism). The Elsasser number is in this case close to unity, but grows slowly as Ta1'2. Restricting ourselves to strictly dipole-type magnetic fields we find for Ta = 108, magnetic cycles with migrating field belts close to the equator. For smaller Taylor numbers and only slightly supercritical a-effect the magnetic field is steady and the Ω-effect becomes unimportant for the generation of toroidal field from a poloidal one. However, magnetic cycles are still possible if the α-effect is sufficiently strong. In this case the field is concentrated at high latitudes. Poloidal and toroidal fields can be in antiphase with equatorward field migration only when the angular velocity increases inwards and towards the poles. The energy of the mean magnetic field generated is usually less than the energy of the turbulent convective motions. The ratio between cycle period and rotational period can reach values of around fifty.

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