Implicit large-eddy simulations of global solar convection: Effects of numerical resolution in nonrotating and rotating cases

Simulating deep solar convection and its coupled mean-field motions is a formidable challenge where few observational results constrain models that suffer from the nonphysical influence of the grid resolution. We present hydrodynamic global implicit large-eddy simulations of deep solar convection performed with the EULAG-MHD code, and we explore the effects of grid resolution on the properties of rotating and nonrotating convection. The results, based on low-order moments and turbulent spectra, reveal that convergence in nonrotating simulations may be achieved at resolutions not much higher than these considered here. The flow is highly anisotropic, with the energy contained in horizontal divergent motions exceeding their radial counterpart by more than three orders of magnitude. By contrast, in rotating simulations, the largest energy is in the toroidal part of the horizontal motions. As the grid resolution increases, the turbulent correlations change in such a way that a solar-like differential rotation, obtained in the simulation with the coarser grid, transitions to an antisolar differential rotation. The reason for this change is the contribution of the effective viscosity to the balance of the forces driving large-scale flows. As the effective viscosity decreases, the angular momentum balance improves, yet the force balance in the meridional direction lessens, favoring a strong meridional flow that advects angular momentum toward the poles. The results suggest that obtaining the correct distribution of angular momentum may not be a mere issue of numerical resolution. Accounting for additional physics, such as magnetism or the near-surface shear layer, may be necessary in simulating the solar interior.