Current state-of-the-art models of the solar convection zone consist of solutions to the Navier–Stokes equations in rotating, 3D spherical shells. Such models are highly sensitive to the choice of boundary conditions. Here we present two suites of simulations differing only in their outer thermal boundary condition, which is either one of fixed entropy (FE) or fixed flux (FF; corresponding to a fixed gradient in the entropy). We find that the resulting differential rotation is markedly different between the two sets. The FF simulations have strong differential rotation contrast and isocontours tilted along radial lines (in good agreement with the Sun’s interior rotation revealed by helioseismology), whereas the FE simulations have weaker contrast and contours tilted in the opposite sense. We examine in detail the force balances in our models and find that the poleward transport of heat by Busse columns drives a thermal wind responsible for the different rotation profiles. We conclude that the Sun’s strong differential rotation along radial lines may result from the solar emissivity being invariant with latitude (which is similar to the FF condition in our models) and the poleward transport of heat by Busse columns. In future work on convection in the solar context, we strongly advise modelers to use an FF outer boundary condition.

The dynamical origins of the Sun's tachocline and near-surface shear layer (NSSL) are still not well understood. We have attempted to self-consistently reproduce a NSSL in numerical simulations of a solar-like convection zone by increasing the density contrast across rotating, 3D spherical shells. We explore the hypothesis that high density contrast leads to near-surface shear by creating a rotationally unconstrained layer of fast flows near the outer surface. Although our high-contrast models do have near-surface shear, it is confined primarily to low latitudes (between ±15 • ). Two distinct types of flow structures maintain the shear dynamically: rotationally constrained Busse columns aligned with the rotation axis and fast, rotationally unconstrained downflow plumes that deplete angular momentum from the outer fluid layers. The plumes form at all latitudes, and in fact are more efficient at transporting angular momentum inward at high latitudes. The presence of Busse columns at low latitudes thus appears essential to creating near-surface shear in our models. We conclude that a solar-like NSSL is unobtainable from a rotationally unconstrained outer fluid layer alone. In numerical models, the shear is eliminated through the advection of angular momentum by the meridional circulation. Therefore, a detailed understanding how the solar meridional circulation is dynamically achieved will be necessary to elucidate the origin of the Sun's NSSL.

The calling card of solar magnetism is the sunspot cycle, during which sunspots regularly reverse their polarity sense every 11 years. However, a number of more complicated time-dependent behaviors have also been identified. In particular, there are temporal modulations associated with active longitudes and hemispheric asymmetry, when sunspots appear at certain solar longitudes or else in one hemisphere preferentially. So far, a direct link between between this asymmetric temporal behavior and the underlying solar dynamo has remained elusive. In this work, we present results from global, 3D magnetohydrodynamic (MHD) simulations, which for the first time display both behavior reminiscent of the sunspot cycle (regular polarity reversals and equatorward migration of internal magnetic field) and asymmetric, irregular behavior that in the simulations we interpret as active longitudes and hemispheric asymmetry. The simulations are thus bistable, in that the turbulent convection can stably support two distinct flavors of magnetism at different times, in superposition, or with smooth transitions from one state to the other. We discuss this new family of dynamo models in the context of the extensive observations of the Sun's surface magnetic field with the Solar and Heliospheric Observatory (SOHO) and the Solar Dynamics Observatory (SDO), as well as earlier observations of sunspot number and synoptic maps. We suggest that the solar dynamo itself may be bistable in nature, exhibiting two types of temporal behavior in the magnetic field.