Super‐rotation and diffusion of axial angular momentum: II. A review of quasi‐axisymmetric models of planetary atmospheres

Abstract The role of angular momentum quasi‐conservation in generating and maintaining axisymmetric flows characterized by a net global and/or local super‐rotation is reviewed. The conditions under which angular momentum per unit mass, m , can be diffused by Newtonian viscosity against its mean gradient in the meridional plane in a compressible, spherical fluid shell are explored in detail, and integral constraints on the form of the diffusive flux of m are derived for a steady flow. The implications of the results for simple models of planetary and stellar atmospheres are explored, with particular reference to the analogy between molecular and ‘eddy’ viscosity (as represented in mixing‐length theory), and various mixing hypotheses for eddy transfer properties. The results are relevant to zonally‐averaged models of the circulation of planetary and stellar atmospheres since, in the absence of molecular viscosity, the Eliassen—Palm flux of m must obey similar integral constraints to those applicable to the viscous flux in a purely axisymmetric system. Despite the non‐Newtonian character of realistic eddies in a baroclinic atmosphere, therefore, studies of simple axisymmetric systems with viscous diffusion can shed some useful insight into ways in which atmospheres, such as those of the earth, Venus, Titan, the Jovian planets and the sun, may acquire significant components of super‐rotation and prograde differential rotation, especially (though not exclusively) near the equator.