Effects of an outer stably stratified layer on equatorial surface flows induced by thermal convection in a rotating spherical shell

In order to explain the equatorial superrotation states observed in Jupiter, Saturn and the sun, possible roles of thermal convection in rotating spherical shells have been investigated. Most of the studies on thermal convection in rotating spherical shells consider situations in which the entire layer is thermally unstable. However, the actual planetary atmospheres may not consist of entirely unstable layers. There exist stable stratospheres and possibly moderately stable cloud layers. Below the cloud layer, the Galileo spacecraft observed a stable layer between depths of 5 and 16 bars in the Jovian atmosphere. If such a stable layer exists near the outer boundary, the generation of surface prograde mean zonal flows caused by the angular momentum transport due to the tilting of columnar convection cells might not operate. Therefore, in the present study, we perform systematic numerical experiments of finite amplitude thermal convection in a rotating spherical shell with an outer stably stratified layer. The Ekman number, the Prandtl number, and the inner/outer radius ratio of the shell are fixed to 10^-3, 1, and 0.4, respectively. The Rayleigh number is varied from a few times to approximately forty times the critical value. The temperature gradient in the stable layer is increased from 1 to 10⁴ times that of the inner unstable layer. The conditions at the boundaries are free-slip and fixed temperature. The time integrations are started from the state of rest accompanied by a point-like temperature disturbance, and continue until the kinetic energy becomes almost stationary. The results show that the existence of a strongly stratified upper layer enhances the generation of equatorial surface retrograde flows when he Rayleigh number is approximately ten times larger than the critical value. These retrograde flows are not associated with the homogenization of angular momentum. It could be explained by change of an effective outer boundary condition operating on the convective motion in the inner layer. The existence of the stable layer causes the bottom of the stable layer to behave as a virtual boundary for the convective motion underneath. Its effective dynamic condition varies from the free-slip condition to the no-slip condition as the Rayleigh number increases. The Reynolds stress of the convective vortices beneath the stable layer is weakened and is dominated by the transport of the planetary angular momentum. As a result, the latitudinal temperature gradient produced at the bottom of the stable layer induces the equatorial retrograde flow. This diffuses through the stable layer by viscosity and produces the equatorial surface retrograde flow.