| Abstract |
This paper presents a theoretical estimation of the strength of equatorial superrotation in planetary atmospheres by exploring a quasi-axisymmetric system which is zonally averaged primitive equations for a dry Boussinesq fluid on a rotating hemisphere with the effects of non-axisymmetric eddies parameterized by eddy diffusion. The fluid is forced by Newtonian heating and cooling, and the horizontal eddy diffusion of momentum is assumed to be much stronger than the vertical one. In this system, the superrotation is maintained by the Gierasch mechanism, which possibly explains the superrotation of the Venus atmosphere by angular momentum transport due to the mean meridional circulation and the horizontal diffusion. For the estimation, a quintic equation for a scalar measure of the superrotation strength is developed from the primitive equations. The quintic equation estimates the superrotation strength by its unique positive solution, which depends only on three non-dimensional parameters: the external thermal Rossby number, the ratio of the radiative relaxation time to the timescale for vertical eddy diffusion of momentum, and the ratio of the planetary rotation period to the geometric mean of the timescales for horizontal and vertical eddy diffusion of momentum. The parameter dependence of the dominant dynamical balance is also investigated by simplifying the quintic equation into a cubic equation. The estimation is verified by comparison with the superrotation strength obtained from numerical solutions of the primitive equations for a wide parameter range covering many orders of magnitude. |
