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Abstract: Three-dimensional studies of convection in deep spherical shells have beenused to test the hypothesis that the strong jet streams on Jupiter, Saturn,Uranus, and Neptune result from convection throughout the molecular envelopes.Due to computational limitations, these simulations must adopt viscosities andheat fluxes many orders of magnitude larger than the planetary values. Severalnumerical investigations have identified trends for how the mean jet speedvaries with heat flux and viscosity, but no previous theories have beenadvanced to explain these trends. Here, we show using simple arguments that ifconvective release of potential energy pumps the jets and viscosity damps them,the mean jet speeds split into two regimes. When the convection is weaklynonlinear, the equilibrated jet speeds should scale approximately with F-nu,where F is the convective heat flux and nu is the viscosity. When theconvection is strongly nonlinear, the jet speeds are faster and should scaleapproximately as F-nu^{1-2}. We demonstrate how this regime shift cannaturally result from a shift in the behavior of the jet-pumping efficiencywith heat flux and viscosity. Moreover, the simulations hint at a third regimewhere, at sufficiently small viscosities, the jet speed becomes independent ofthe viscosity. We show based on mixing-length estimates that if such a regimeexists, mean jet speeds should scale as heat flux to the 1-4 power. Ourscalings provide a good match to the mean jet speeds obtained in previousBoussinesq and anelastic, three-dimensional simulations of convection withingiant planets over a broad range of parameters. When extrapolated to the realheat fluxes, these scalings suggest that the mass-weighted jet speeds in themolecular envelopes of the giant planets are much weaker-by an order ofmagnitude or more-than the speeds measured at cloud level.

Author: Adam P. Showman, Yohai Kaspi, Glenn R. Flierl


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