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. 253

On the Amplitude of Convective Velocities in the Deep Solar Interior

“…In this Appendix we demonstrate further that baroclinicity alone cannot account for the solar differential rotation as inferred from helioseismology. Similar issues have been studied for decades within the context of planetary and stellar atmospheres (Eliassen 1951;Read 1986;Tassoul 1978).…”

“…It is clear from equations (1) and (3) that both mechanical and thermal forcing, F and Q, can induce a meridional circulation. Indeed, this is a classical problem in the theory of planetary and stellar atmospheres (Eliassen 1951;Read 1986;Tassoul 1978). In a solar context, eq.…”

Voyager 2 in the Uranian System: Imaging Science Results

“…8 suggests that the atmosphere rotates more slowly than the magnetic field within 20°of the equator. An equatorial subrotation of this sort was predicted by Read (13) from models of axisymmetric circulations.…”

Equatorial superrotation in Held and Suarez like flows with weak equator‐to‐pole surface temperature gradient

“… at the surface), a zonally symmetric mean meridional circulation conserves M such that M ≤ M 0 at all latitudes in the absence of sources and sinks. In general, superrotation can be generated if there is a process that provides a steady eddy angular momentum flux directed up the meridional gradient of the angular momentum, a −1 ∂M φ / ∂φ (Hide, ; see also Read, ).…”