The profile of the differential rotation together with the sign of the alpha-effect determine the dynamo wave direction. In early models of the solar dynamo the dynamo wave often leads to a poleward migration of the activity belts. Flux transport by the meridional flow or the effect of the surface shear layer are possible solutions. In a model including the corona, we show that various migrations can be obtained by varying the properties of the corona. A new dynamo of Babcock-Leighton type also leads to the correct equatorward migration by the non-linear relation between flux density and rise time of the flux.

The sunspot cycle is quite variable in duration and amplitude, yet in the long term, it seems to return to solar minimum on schedule, as if guided by a clock with an average period of close to 11.05 years for the sunspot number cycle and 22.1 years for the magnetic cycle. This paper provides a brief review of the sunspot number cycle since 1750, discusses some of the processes controlling the solar dynamo, and provides clues that may add to our understanding of what controls the cadence of the solar clock.

We consider several tracers of magnetic activity that separate cycle-dependent contributions to the background solar magnetic field from those that are independent of the cycle. The main message is that background fields include two relative separate populations. The background fields with a strength up to 100 Mx cm−2 are very poorly correlated with the sunspot numbers and vary little with the phase of the cycle. In contrast, stronger magnetic fields demonstrate pronounced cyclic behaviour. Small-scale solar magnetic fields demonstrate features of fractal intermittent behaviour, which requires quantification. We investigate how the observational estimate of the solar magnetic flux density B depends on resolution D in order to obtain the scaling In BD = −k In D + a in a reasonably wide range. The quantity k demonstrates cyclic variations typical of a solar activity cycle. k depends on the magnetic flux density, i.e. the ratio of the magnetic flux to the area over which the flux is calculated, at a given instant. The quantity a demonstrates some cyclic variation, but it is much weaker than in the case of k. The scaling is typical of fractal structures. The results obtained trace small-scale action in the solar convective zone and its coexistence with the conventional large-scale solar dynamo based on differential rotation and mirror-asymmetric convection. Here we discuss the message for solar dynamo studies hidden in the above results.

We could find a new 5 year periodicity in the occurrences of peaks in sunspot activity and inferred deviations of annual Indian monsoon rainfall variations from the normal during the Maunder minimum (MM) period. This result is explained in terms of solar dynamo functioning in a different mode from normal during the MM where quadrupole field (first harmonic, 5-5.5 years) dominate over dipole field (fundamental, 11 years) causing extreme north south asymmetry in sunspot activity.

We could identify three categories of solar proton events (SPE) with distinct solar origin from an analysis of direct and indirect observations during the years 1561-2016 CE spanning 42 sunspot cycles. They are (i) 10 MeV SPE whose number of occurrences closely follow the sunspot cycles (ii) 30 MeV SPE which show secular changes with peaks near Gleissberg solar cycle minima and inferred to be associated with distinct enhancements in the efficiency of the solar dynamo and (iii) those associated with Impulsive and irregular solar activity changes such as the Carrington event of September 1859. The relevance of above results for stars exhibiting cyclic and irregular activity changes will be also discussed.

Kinematic solar dynamo models (KSDM) that use a solar like differential rotation profile usually fail to reproduce the latitudinal distribution of the toroidal magnetic fields. Usually, it is assumed that it is the larger radial shear present in the solar tachocline at higher latitudes that is the responsible for such results. We here consider variations in the shape and thickness of the tachocline and find that a better distribution of the toroidal fields is obtained when the thickness of the tachocline is $d_1=0.02R_{\odot}$, a smaller value than that conventionally used.

Mean-field and direct simulations of the hydrodynamics and hydromagnetics of the solar convection zone are discussed with the ultimate aim to understand the generation of differential rotation and magnetic fields. Various arguments constraining the values of the various turbulent diffusion coefficients are presented. It is suggested that the turbulent magnetic diffusivity is much smaller than the eddy viscosity which, in turn, is by up to a factor of ten smaller than the eddy conductivity. The magnetic field obtained from direct simulations is highly intermittent, and there is no clear systematic orientation of bipolar regions emerging from the convection zone. Various mechanisms that might cause such a field orientation are considered. Finally, the application of direct simulations to the determination of mean-field transport coefficients is emphasised.