Convection driven magnetohydrodynamic dynamos in rotating spherical shells

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Abstract
Finite amplitude solutions for magnetohydrodynamic dynamos driven by convection in rotating spherical fluid shells with a radius ratio of ηequals; 0.4 are obtained numerically by the Galerkin method. Solutions which are twice periodic in the azimuth (case m equals; 2) are emphasized, but a few cases with higher azimuthal wavenumber have also been considered. An electrically insulating space outside the fluid shell has been assumed. A comparison of the dynamo solutions of both, dipolar and quadrupolar, symmetries with the corresponding non-magnetic solutions shows a strong increase of the amplitude of convection owing to the release of the rotational constraint by the Lorentz force. In some cases at low Taylor number the amplitude of convection is decreased, however, owing to the competition of the magnetic degree of freedom for the same energy source. The strength of differential rotation is usually reduced by the Lorentz force, especially in the case of quadrupolar dynamos which differ in this respect from dipolar dynamos for topological reasons. Some preliminary results on the stability of the steady dynamo solutions are also presented.

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