A variance analysis of angular momentum in stellar and planetary atmospheres

For purposes of studying the dynamics of stellar and planetary atmospheres, a system of balance equations is derived for the square of the absolute angular momentum, for the square of its zonal average and for its variance along the length of closed latitude circles. Pressure and frictional forces are included, but magnetic effects are not considered at present. As discussed by the first author previously, limitations on possible axisymmetric flows lead to criteria defining forbidden regimes. Physical pictures of the manner in which nonzonal eddies alter the variance of angular momentum are outlined for certain systems. An argument is made to suggest that thermal forcing of the pure eddy type (perhaps like Rayleigh convection) tends to establish an equatorial acceleration in stellar and certain planetary atmospheres, through negative eddy viscous effects. A significantly more general set of balance equations is derived in an appendix.