Two fundamentally different views of the general circulation of Jovian atmospheres have emerged. According to one view, the observed jet streams at the cloud tops are controlled by the vorticity transfers of small scale eddies generated by planetary wave instabilities within a shallow atmospheric layer. According to the alternate point of view, the zonal jets are surface manifestations of deep interior convection organized into cylindrical motion with axes parallel to the planetary rotation axis. Both approaches may be considered in the context of the very different roles assumed by the potential vorticity. A possible reconciliation of the two kinds of dynamical systems is considered in which the interior motion is overlaid with a statically stable cappling layer driven by turbulent energy injection from below. A simple model for the eddy driving of quasi-geostrophic dynamics in the capping layer is presented which is consistent with the tentative evidence for up-gradient momentum flux on Jupiter and IRIS observations of thermal contrast correlations with cyclonic and anticyclonic shear zones. Certain synoptic-scale cloud features in Jupiter's atmosphere are interpreted as breaking waves, which may also influence the lateral mixing of tracers such as the ortho-para hydrogen ratio.