Three‐dimensional Spherical Simulations of Solar Convection. I. Differential Rotation and Pattern Evolution Achieved with Laminar and Turbulent States

Abstract

Rotationally constrained convection possesses velocity correlations that transport momentum and drive mean —ows such as diUerential rotation. The nature of this transport can be very complex in turbu- lent —ow regimes, where large-scale, coherent vorticity structures and mean —ows can be established by smaller scale turbulence through inverse cascades. The dynamics of the highly turbulent solar convection zone therefore may be quite diUerent than in early global-scale numerical models, which were limited by computational resources to nearly laminar —ows. Recent progress in high-performance computing tech- nology and ongoing helioseismic investigations of the dynamics of the solar interior have motivated us to develop more sophisticated numerical models of global-scale solar convection. Here we report three- dimensional simulations of compressible, penetrative convection in rotating spherical shells in both laminar and turbulent parameter regimes. The convective structure in the laminar case is dominated by ii banana cells,ˇˇ but the turbulent case is much more complex, with an intricate, rapidly evolving down- —ow network in the upper convection zone and an intermittent, plume-dominated structure in the lower convection zone and overshoot region. Convective patterns generally propagate prograde at low lati- tudes and retrograde at high latitudes relative to the local rotation. The diUerential rotation pro—les show some similarity with helioseismic determinations of the solar rotation but still exhibit signi—cantly more cylindrical alignment. Strong, intermittent, vortical down—ow lanes and plumes play an important dynamical role in turbulent —ow regimes and are responsible for signi—cant diUerences relative to laminar —ows with regard to momentum and energy transport and to the structure of the overshoot region at the base of the convection zone. Subject headings: convectionhydrodynamicsstars: interiorsSun: interiorSun: rotation ¨ turbulence