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Super-rotation is a common phenomenon in solar system planetary atmospheres. Out of the four substantial atmospheres possessed by solid bodies in the solar system, the slowly rotating planet, Venus, and moon, Titan, are both well-known to have atmospheres that rotate on average substantially more quickly than does the solid surface underneath. The more rapidly rotating planets, Mars and Earth, have much weaker global super-rotation, but both can exhibit time-varying prograde jets near the equator which rotate more rapidly than the local surface. Atmospheric super-rotation is not restricted to planets with solid surfaces and shallow atmospheres. Cloud-tracking observations of the gas giants Jupiter and Saturn show that they both possess rapid prograde equatorial jets and hence exhibit local super-rotation.\ud \ud Simplified global circulation models of extra-solar planets, including representations of ‘hot Jupiters’ and Earth-like planets rotating at different rates, can also show sustained super-rotating equatorial jets in different dynamical regimes. In the extra-solar planet cases in particular, the quantitative results are highly sensitive to model parameters. \ud \ud In each case the detailed mechanism, or combination of mechanisms, which produces the super-rotating jets might vary, but all require longitudinally asymmetric motions, waves or eddies, to transport angular momentum up-gradient into the jets. The mechanism is not always easy to diagnose from observations and requires careful modelling. We review both observations of solar system planets and recent global circulation model results, combined in the case of Mars and Earth in the form of atmospheric reanalyses by data assimilation, together with simplified extra-solar planet simulations.

We compare five general circulation models (GCMs) which have been recently used to study hot extrasolar planet atmospheres (BOB, CAM, IGCM, MITgcm, and PEQMOD), under three test cases useful for assessing model convergence and accuracy. Such a broad, detailed intercomparison has not been performed thus far for extrasolar planets study. The models considered all solve the traditional primitive equations, but employ di↵erent numerical algorithms or grids (e.g., pseudospectral and finite volume, with the latter separately in longitude-latitude and ‘cubed-sphere’ grids). The test cases are chosen to cleanly address specific aspects of the behaviors typically reported in hot extrasolar planet simulations: 1) steady-state, 2) nonlinearly evolving baroclinic wave, and 3) response to fast timescale thermal relaxation. When initialized with a steady jet, all models maintain the steadiness, as they should—except MITgcm in cubed-sphere grid. A very good agreement is obtained for a baroclinic wave evolving from an initial instability in pseudospectral models (only). However, exact numerical convergence is still not achieved across the pseudospectral models: amplitudes and phases are observably di↵erent. When subject to a typical ‘hot-Jupiter’-like forcing, all five models show quantitatively di↵erent behavior—although qualitatively similar, time-variable, quadrupole-dominated flows are produced. Hence, as have been advocated in several past studies, specific quantitative predictions (such as the location of large vortices and hot regions) by GCMs should be viewed with caution. Overall, in the tests considered here, pseudospectral models in pressure coordinate (PEBOB and PEQMOD) perform the best and MITgcm in cubed-sphere grid performs the worst.