[42] We have constructed relatively simple numerical models that describe a self-sustained process of generation of interacting global and local magnetic fields. As in most hypothetical astrophysical dynamos, the generation is driven by thermal convection in combination with differential rotation. We did not introduce any kinematic elements in our model, so that the entire velocity field appeared as the solution of the full system of MHD equations.
[43] The most remarkable features revealed in the computed dynamo regimes can be summarized as follows. The process of magnetic field generation is cyclic, although rather irregular. It includes the repeated generation of local, in many cases bipolar, magnetic structures. These structures dissipate giving rise to chaotic background fields. They may drift in the poleward direction, replacing the already existing, "old" background fields. In some cases, a correspondence can be noted between such polarity reversals in the polar regions and sign reversals of the axisymmetric bipolar component of the global magnetic field.
[44] One of the computed scenarios demonstrates a remarkable intermittency in the behavior of some fractions of magnetic energy: the axisymmetric and the nonaxisymmetric part of the magnetic field component with a dipolar symmetry alternate in making larger contributions to the total energy peaks.
[45] Mean-field dynamo models, which have been most popular in astrophysics over a few past decades, attribute the generation of the global magnetic fields of stars to the a effect, the statistical predominance of one sign of the velocity field helicity over another. It is quite plausible that the a effect, in one form or another, is a fairly general property of various velocity fields capable of maintaining undamped regular magnetic fields. However, this property must not necessarily be associated with turbulent motion. In particular, the model velocity field in the toroidal eddies used by Getling and Tverskoy [1971a, 1971b] to construct a global dynamo included an azimuthal (with respect to the axis of the eddy) velocity component, so that the trajectories of the fluid particles were spirals deformed in a certain way. A similar property may also be inherent in the convective flow that develops in our model, although checking this possibility requires a special investigation.
[46] At this stage, the "deterministic" cellular dynamo described here is oversimplified to be regarded as a model of the solar or any other specific stellar dynamo. However, it demonstrates that the dynamics of the well-structured local magnetic fields and of the global magnetic field may be ingredients of one complex process.
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