On rotationally driven meridional flows in stars

A quasi-steady-state model of the consequences of rotation on the hydrodynamical structure of a stellar radiative zone is derived by studying in particular the role of centrifugal and baroclinic driving of meridional motions in angular momentum transport. This non-linear problem is solved numerically, assuming axial symmetry of the system, and within some limits it is shown that there exist simple analytical solutions. The limit of slow rotation recovers Eddington-Sweet theory, whereas it is shown that in the limit of rapid rotation the system settles into a geostrophic equilibrium. The behaviour of the system is found to be controlled by one parameter only, linked to the Prandtl number, the stratification and the rotation rate of the star.