Differential Rotation and Convection in the Sun

The differential rotation profile of the solar convection zone (SCZ), apart from inner and outer boundary layers, can be accurately reproduced if the isorotation contours correspond to the characteristics of the vorticity equation in its thermal wind form. The analytic structure of these characteristics is transparent, and surprisingly simple.
The very existence of the characteristics, however, requires that there be a formal functional relationship involving the entropy and the angular velocity. In this talk, I will specify this relationship, and explain how it may arise naturally from the dynamics of convection and differential rotation. Direct support for the entropy/angular velocity relationship can be adduced from published numerical simulations of the SCZ. More generally, this "thermal wind characteristic theory" can also be used diagnostically for the internal entropy structure of the SCZ, and may be extended to fully convective stars of low convective Rossby number.