From Penetrative Convection to Teleconvection

In the deep interiors of rapidly rotating stars and planets the Coriolis force plays an essential role in determining the depth of penetrative convection from a convectively unstable region into a neighboring stably stratified region. The linear Coriolis force, not the nonlinear inertial force, dominates the dynamics. Accordingly, this paper investigates linear penetrative convection in a rapidly rotating, convectively unstable plane or spherical fluid layer bounded above by a less unstable or a stable corotating plane or spherical fluid layer. For the plane-layer geometry, exact solutions are obtained for two stress-free bounding walls. Asymptotic relations for the onset of penetrative convection in a rapidly rotating plane-layer system are obtained for an asymptotically small Ekman number. It is shown that the interface between the stable and unstable layer forms an effective wall that prevents convective flows from penetrating deeply into the stable fluid layer. This is the ordinary situation of penetrative convection. In spherical-layer geometry, the problem is fundamentally different. Several new and novel forms of convection are discovered. In one phenomenon that we term teleconvection, convection is thermally driven in the deep unstable interior, but the resulting convective motions concentrate primarily in the stable region near the outer spherical surface far away from the location of the thermal forcing. In another case we find a multilayer roll structure in rotating spherical two-layer convection as a result of a stable spherical outer layer. Our findings suggest that observed motions in the atmospheres of planets or stars could be driven by remote energy sources in their deep interiors.