Some of these simulations are now beginning to yield regular polarity reversals of the large-scale magnetic components. Figures 20 and 21 present some sample results taken from Ghizaru et al. (2010), see also Brown et al. (2009) and Käpylä et al. (2010). Figure 20 is an animation in Mollweide latitude-longitude projection of the toroidal magnetic component below the nominal interface between the convecting layers and underlying stable layers in one of these simulations. This toroidal component reaches some 2.5 kG here, and shows a very clear global antisymmetry about the equator, despite strong spatiotemporal fluctuations produced by convective undershoot. The cyclic variation of this large-scale field is quite apparent on the animation, with polarity reversals approximately synchronous across hemispheres.
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Figure 21A shows, for the same simulation as in Figure 20, a time-latitude diagram of the zonally-averaged toroidal component, now constructed at a depth corresponding to the core-envelope interface in the model. This is again assumed to be the simulation’s equivalent to the sunspot butterfly diagram. This simulation was run for 255 yr, in the course of which eight polarity reversals have taken place, with a mean (half-)period of about 30 yr. Note the tendency for equatorward migration of the toroidal flux structures, and the good long-term synchrony between the Northern and Southern hemispheres, persisting despite significant fluctuations in the amplitude and duration of cycles in each hemiphere. Figure 21B shows the corresponding time-evolution of the zonaly-averaged radial surface magnetic component, again in a time-latitude diagram. The surface field is characterized by a well-defined dipole moment aligned with the rotational axis, with transport of surface fields taking place from lower latitudes and (presumably) contributing to the reversal of the dipole moment. Compare these time-latitude diagrams to the sunspot butterfly diagram of Figure 3 and synoptic magnetogram of Figure 4, and reflect upon the similarities and differences.
Although much remains to be investigated regarding the mode of dynamo action in these simulations, some encouraging links to mean-field theory (Section 3.2.1) do emerge. The fact that a positive toroidal component breeds here a positive dipole moment is what one would expect from a turbulent -effect (more precisely, the tensor component) positive in the Northern hemisphere. A posteriori calculation of the mean electromotive force does reveal a clear hemispheric pattern, with having the same sign in both hemisphere, but changing sign from one cycle to the next, again consistent with the idea that the turbulent -effect is the primary source of the large-scale poloidal component. Likewise, having a well-defined axisymmetric dipolar component being sheared by an axisymmetric differential rotation is consistent with the buildup of a large-scale toroidal component antisymmetric about the equatorial plane.
On the other hand, calculation of the and -components of the mean electromotive force indicates that the latter contributes to the production of the toroidal field at a level comparable to shearing of the poloidal component by differential rotation, suggestive of what, in mean-field electrodynamics parlance, is known as an dynamo. Calculation of the -tensor components also reveals that the latter do not undergo significant variations between maximal and minimal phases of the cycle, suggesting that -quenching is not the primary amplitude-limiting mechanism in this specific simulation run. Although it would premature to claim that these simulations vindicate the predictions of mean-field theory, to the level at which they have been analyzed thus far, they do not appear to present outstanding departures from the mean-field Weltanschau.
Living Rev. Solar Phys. 7, (2010), 3
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