Jupiter’s turbulent weather layer contains phenomena of many different sizes, from local storms up to the Great Red Spot and banded jets. The global circulation is driven by complex interactions with (as yet uncertain) small-scale processes. We have calculated structure functions and kinetic energy spectral fluxes from Cassini observations over a wide range of length scales in Jupiter’s atmosphere. We found evidence for an inverse cascade of kinetic energy from length scales comparable to the first baroclinic Rossby deformation radius up to the global jet scale, but also a forward cascade of kinetic energy from the deformation radius to smaller scales. This second result disagrees with the traditional picture of Jupiter’s atmospheric dynamics, but has some similarities with mesoscale phenomena in the Earth’s atmosphere and oceans. We conclude that the inverse cascade driving Jupiter’s jets may have a dominant energy source at scales close to the deformation radius, such as baroclinic instability.