A model of mean zonal flows in the major planets

摘要

A mathematical model is developed for the generation of mean zonal flows by thermal convection in rapidly rotating, self-gravitating spheres. The analysis is based on an expansion of the basic equations in terms of the Prandtl numberP, the amplitudeAof convection, and the parameter #x3F5; which is related to the curvature of the spherical surface. Mean zonal flows of the orderPA2#x3F5;are found. Although the Boussinesq approximation is used throughout the analysis, the results compare reasonably well with the observations of zonal flows in the atmospheres of Jupiter and Saturn. In particular, the fact that the amplitude of the Jovian equatorial jet is low in comparison with the corresponding jet on Saturn is explained in terms of the low equatorial convective heat flux on Jupiter.