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The weather layers of the gas giant planets, Jupiter and Saturn, comprise theshallow atmospheric layers that are influenced energetically by a combinationof incoming solar radiation and localised latent heating of condensates, aswell as by upwelling heat from their planetary interiors. They are also themost accessible regions of those planets to direct observations. Recentanalyses in Oxford of cloud-tracked winds on Jupiter have demonstrated thatkinetic energy is injected into the weather layer at scales comparable to theRossby radius of deformation and cascades both upscale, mostly into theextra-tropical zonal jets, and downscale to the smallest resolvable scales inCassini images. The large-scale flow on both Jupiter and Saturn appears toequilibrate towards a state which is close to marginal instability according toArnol'd's 2nd stability theorem. This scenario is largely reproduced in ahierarchy of numerical models of giant planet weather layers, includingrelatively realistic models which seek to predict thermal and dynamicalstructures using a full set of parameterisations of radiative transfer,interior heat sources and even moist convection. Such models include the JasonGCM, developed in Oxford, which also represents the formation of (energeticallypassive) clouds of NH3, NH4SH and H2O condensates and the transport ofcondensable tracers. Recent results show some promise in comparison withobservations from the Cassini and Juno missions, but some observed features(such as Jupiter's Great Red Spot and other compact ovals) are not yet capturedspontaneously by any weather layer model. We review recent work in this veinand discuss a number of open questions for future study.

The turbulent dynamics of Jupiter's and Saturn's weather layers: order out of chaos?