The Sun, our nearest late-type star exhibits a magnetic activity cycle with a period of around 11 yr. The cyclic magnetic field is generated by a dynamo operating below the surface, where it converts the energy of rotating convective turbulence into magnetic energy. We are still far from fully understanding the solar dynamo mechanism (e.g., Ossendrijver 2003; Charbonneau 2014). One reason is the limited information about the dynamics in the solar convection zone. Helioseismology has provided us with the profile of temperature and density stratification and the differential rotation (e.g., Schou et al. 1998) in the interior. Further information, such as the meridional circulation profiles, convective velocity strength, or even magnetic field distributions, are currently inconclusive or not even possible (e.g., Basu 2016; Hanasoge et al. 2016). One way to investigate how important differential rotation, meridional circulation, and turbulent convective velocities are for the solar dynamo is to use numerical simulations. Since the early simulations by Gilman (1983), the increase of computing resources has prompted several advances using numerical simulations. Nowadays, global simulations of convective dynamos are able to reproduce cyclic magnetic fields and dynamo solutions resembling many features of the solar magnetic field evolution (Ghizaru et al. 2010; Käpylä et al. 2012; Warnecke et al. 2014; Augustson et al. 2015), even long-time evolution (Augustson et al. 2015; Käpylä et al. 2016; Beaudoin et al. 2016). The cyclic magnetic field in these simulations can be well understood in terms of Parker–Yoshimura rule (Parker 1955; Yoshimura 1975; Warnecke et al. 2014), in which a propagating αΩ dynamo wave is excited; see also Gastine et al. (2012). The α effect (Steenbeck et al. 1966) describes the magnetic field enhancement from helical turbulence and the Ω effect the shearing of magnetic field caused by differential rotation. The propagation direction of the dynamo wave depends on the sign of α and shear: to generate an equatorward propagating wave, the product of α and the radial gradient of Ω must be negative (positive) in the northern (southern) hemisphere. Explaining the solar equatorward propagation of the sunspot appearance by the Parker–Yoshimura rule therefore requires either invoking the near-surface-shear layer (Brandenburg 2005), because the radial gradient is only negative in that layer (Barekat et al. 2014) and α is positive, or changing the sign of α in the bulk of the convection zone (Duarte et al. 2016) where the radial shear is positive. Furthermore, to understand the magnetic field evolution fully in the global numerical simulation one needs suitable analysis tools to extract the important contribution of turbulent dynamo effects. One of these tools is the test-field method (Schrinner et al. 2005, 2007; Warnecke et al. 2018). This method allows the determination of the turbulent transport coefficients directly from the simulations. This includes the measurement of tensorial coefficients such as α, turbulent pumping, and turbulent diffusion. The first application to global convection simulations of solar-like dynamo has already revealed that the turbulent effects can have a significant impact on large-scale magnetic field dynamics (Warnecke et al. 2018; Gent et al. 2017).
Citation: Käpylä et al. 2012
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