The banded organization of clouds associated with intense zonal (east-west) jet streams and large-scale oval vortices on Jupiter and Saturn have long fascinated astronomers and atmospheric dynamicists for many years. The current view is that these features are a manifestation of strongly anisotropic energy transfers within a highly turbulent fluid on a rapidly rotating, spherical planet that is energised at relatively small scales, either by free convection or baroclinic instabilities, but the details are still not well understood. In this talk we will explore insights from a laboratory experiment on the Coriolis platform in Grenoble that investigated a plausible physical analogue of Jupiter’s atmospheric circulation, energized mainly by free thermal convection with strong background rotation. Weak, eddy-driven jets were obtained through anisotropic energy exchanges, though (for reasons to be discussed) it was not possible to match Jupiter's parameter regime very closely in the laboratory. We will compare the dynamics and energetics of our laboratory experiment with new measurements of energy exchanges, spectra and structure functions in Jupiter’s atmosphere from analysis of Cassini spacecraft images, which indicate some new directions for models of Jupiter’s atmospheric circulation.