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The evolution of unforced and weakly damped two-dimensional turbulence over random rough topography presents two extreme states. If the initial kinetic energy $E$is sufficiently high, then the topography is a weak perturbation, and evolution is determined by the spontaneous formation and mutual interaction of coherent axisymmetric vortices. High-energy vortices roam throughout the domain and mix the background potential vorticity (PV) to homogeneity, i.e., in the region between vortices, which is most of the domain, the relative vorticity largely cancels the topographic PV. If $E$is low, then vortices still form but they soon become locked to topographic features: Anticyclones sit above topographic depressions and cyclones above elevated regions. In the low-energy case, with topographically locked vortices, the background PV retains some spatial variation. We develop a unified framework of topographic turbulence spanning these two extreme states of low and high energy. A main organizing concept is that PV homogenization demands a particular kinetic energy level $E_{♯}$. $E_{♯}$is the separator between high-energy evolution and low-energy evolution. 

Vortex crystals are quasiregular arrays of like-signed vortices in solid-body rotation embedded within a uniform background of weaker vorticity. Vortex crystals are observed at the poles of Jupiter and in laboratory experiments with magnetized electron plasmas in axisymmetric geometries. We show that vortex crystals form from the free evolution of randomly excited two-dimensional turbulence on an idealized polar cap. Once formed, the crystals are long lived and survive until the end of the simulations (300 crystal-rotation periods). We identify a fundamental length scale, L γ = ( U / γ ) 1 / 3 , characterizing the size of the crystal in terms of the mean-square velocity U of the fluid and the polar parameter γ = f p / a p 2 , with f p the Coriolis parameter at the pole and a p the polar radius of the planet. 

Abstract Jupiter’s atmosphere is one of the most turbulent places in the solar system. Whereas observations of lightning and thunderstorms point to moist convection as a small-scale energy source for Jupiter’s large-scale vortices and zonal jets, this has never been demonstrated due to the coarse resolution of pre-Juno measurements. The Juno spacecraft discovered that Jovian high latitudes host a cluster of large cyclones with diameter of around 5,000 km, each associated with intermediate- (roughly between 500 and 1,600 km) and smaller-scale vortices and filaments of around 100 km. Here, we analyse infrared images from Juno with a high resolution of 10 km. We unveil a dynamical regime associated with a significant energy source of convective origin that peaks at 100 km scales and in which energy gets subsequently transferred upscale to the large circumpolar and polar cyclones. Although this energy route has never been observed on another planet, it is surprisingly consistent with idealized studies of rapidly rotating Rayleigh–Bénard convection, lending theoretical support to our analyses. This energy route is expected to enhance the heat transfer from Jupiter’s hot interior to its troposphere and may also be relevant to the Earth’s atmosphere, helping us better understand the dynamics of our own planet.