However, these studies did not investigate large-scale dynamo action. The effect of sub-adiabatic layers in global MHD simulations was investigated by Käpylä et al. (2019). The formation of a stably stratified layer at the bottom of the domain allowed for the storage of magnetic field beneath it, also found in an earlier study by Browning et al. (2006), but these strong fields were also seen to be capable of suppressing the oscillating magnetic field at the surface. Käpylä et al. (2019) also considered the effect of sub-adiabatic layers on the convective velocity spectra, but found that the decrease in power at large scales was not enough to solve this part of the conundrum.
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Another mechanism to reduce the overly high rotational influence on convection in simulations, studied first in a Cartesian model by Hotta et al. (2015) and then in fully spherical models by Karak et al. (2018), could be provided by the Lorentz force feedback from the magnetic to the velocity field. Such feedback could result from strong magnetic fluctuations, originating for example from the action of a small-scale dynamo instability operating in the CZ. Thus-generated magnetic fluctuations could suppress the turbulent velocity field through the Lorentz force, hence acting as an enhanced viscosity, and increasing the magnetic Prandtl number, that is, the ratio of the viscosity and resistivity of the fluid. Karak et al. (2018) investigated such a situation numerically; their simulations developed an overshoot zone at the base of the domain, and also showed a decrease in the convective power at large scales due to downward-directed plumes. These results, although arising for a different reason, are consistent with the results of Käpylä et al. (2017, 2019). Another finding of Karak et al. (2018) was that the plumes, carrying their angular momentum inward, caused the rotation profile to switch to anti-solar.
The aim of this paper is to extend the study of Viviani et al. (2018) to include a dynamically adaptable heat conduction. In order to do this, we use a Kramers-like opacity law, as was done in Käpylä et al. (2019) for semi-spherical wedge simulations. We use computational domains extending over the full longitudinal extent in order to be able to study both axi- and nonaxisymmetric dynamo solutions.
We show the near the surface as a function of time (the so-called butterfly diagram) in Fig. 4. We note that other modelling groups plot their butterfly diagrams from the base of the CZ (e.g., Fan & Fang 2014), but in our case, no migration of the magnetic field occurs there. We show the radial magnetic field in time at the bottom of the CZ in Appendix B. Run R1 is characterized by an equatorially symmetric magnetic field with nonmigrating negative polarities at low latitudes, and a poleward migrating positive field at higher latitudes. A stationary negative field is present at all times close to the latitudinal boundary. A similar, oscillatory dynamo solution was reported and analyzed in detail in Viviani et al. (2019). There, it was concluded that two dynamo modes were competing in the model, a stationary and an oscillatory one, the latter with polarity reversals. These latter authors came to the conclusion that this dynamo is driven mostly by turbulent effects, as the differential rotation was found to be weak in the model. Run R1 appears to be another incarnation of such a dynamo in the transition regime from solar-like to anti-solar differential rotation.
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