Zonal flows and grand minima in a solar dynamo model

Observations of differential rotation within the solar convection zone have revealed a cyclic pattern of zonal shear flows. Given that the 11-yr periodicity of this flow pattern is approximately half that of the 22-yr solar activity cycle, it is likely that these flows are magnetically driven. In this paper, these zonal shear flows are investigated in the context of a parametrized mean-field solar dynamo model which incorporates the feedback of the large-scale magnetic fields upon an imposed differential rotation profile. This 'interface-like' model produces dynamo action and a pattern of zonal flows that is qualitatively consistent with solar observations. One of the key parameters in this model is the magnetic Prandtl number - when this parameter is small, it is possible to find time-dependent solutions that are characterized by prolonged phases of significantly reduced magnetic activity (so-called 'grand minima'). Despite the presence of grand minima, it is still possible to find a solar-like pattern of zonal shear flows in this highly modulated, low magnetic Prandtl number regime.