On spherical mean‐field dynamo models with coupling between axisymmetric and non‐axisymmetric field modes

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Abstract
The mean‐field dynamo models developed on the basis of mean‐field magnetohydrodynamics reflect some essential features of the magnetic phenomena accompanying the Earth, the Sun and other cosmical bodies. The magnetic fields of those objects may be understood as superpositions of modes which are obtained if the fields are subjected to Fourier decomposition with respect to the longitudinal coordinate and each Fourier component is split into two parts which are either symmetric or antisymmetric with respect to the equatorial plane. The mean‐field models investigated so far provide no satisfactory explanation for the distinct multimodal structure of the observed fields. Within the framework of the traditional mean‐field concept, and with reasonable assumptions, possibilities of couplings of modes occur only due the back‐reaction of the magnetic field on the motions. These possibilities are discussed, and results of relevant numerical experiments are presented. It is open to question whether couplings of this kind are able to explain the coexistence of modes of the observed fields. A modified mean‐field concept is proposed which implies couplings of modes even without any back‐reaction. Contrary to the couplings due to back‐reaction these couplings imply that, in general, axisymmetric modes are accompanied by non‐axisymmetric ones.

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