Turbulent convection and differential rotation in spherical shells

Rotation is a general phenomenon in astrophysical systems on scales from planets to giant galaxy clusters. It is established during the formation of the system under gravitational compression. Typically the rotation rate is greatly enhanced during this process (Thompson et al. 2003). Rotation of stars defines their shapes and drives the internal circulation which redistributes chemical elements and angular momentum (Maeder 2009). The differential rotation of the Sun is thought to be a key ingredient of its dynamo, a driver of the 11-year activity cycle (Schrijver & Zwaan 2000). The difference in the speed of sunspots at different latitudes was noticed in Galileo’s first observations of sunspots. Since then differential rotation was observed by tracking different photospheric features and by spectral observations of the limb. The angular speed on the visible surface of the Sun smoothly decreases from the equator to the poles. The approximate law, deduced from observations, is usually in the form of