Zonal flow scaling in rapidly-rotating compressible convection

Abstract

The surface winds of Jupiter and Saturn are primarily zonal. Each planet exhibits strong prograde equatorial flow flanked by multiple alternating zonal winds at higher latitudes. The depth to which these flows penetrate has long been debated and is still an unsolved problem. Previous rotating convection models that obtained multiple high latitude zonal jets comparable to those on the giant planets assumed an incompressible (Boussinesq) fluid, which is unrealistic for gas giant planets. Later models of compressible rotating convection obtained only few high latitude jets which were not amenable to scaling analysis. Here we present 3-D numerical simulations of compressible convection in rapidly-rotating spherical shells. To explore the formation and scaling of high-latitude zonal jets, we consider models with a strong radial density variation and a range of Ekman numbers, while maintaining a zonal flow Rossby number characteristic of Saturn. All of our simulations show a strong prograde equatorial jet outside the tangent cylinder. At low Ekman numbers several alternating jets form in each hemisphere inside the tangent cylinder. To analyse jet scaling of our numerical models and of Jupiter and Saturn, we extend Rhines scaling based on a topographic $\beta$-parameter, which was previously applied to an incompressible fluid in a spherical shell, to compressible fluids. The jet-widths predicted by this modified Rhines length are found to be in relatively good agreement with our numerical model results and with cloud tracking observations of Jupiter and Saturn.

17 pages, 12 figures, 3 tables, accepted for publication in PEPI

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• Jupiter's unearthly jets: a new turbulent model exhibiting statistical steadiness without large-scale dissipation
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• The compressional beta effect: a source of zonal winds in planets?
• Dynamo Action in the Steeply Decaying Conductivity Region of Jupiter-like Dynamo Models
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• A Global Simulation of the Dynamo, Zonal Jets, and Vortices on Saturn
• Decoupling Jupiter's deep and atmospheric flows using the upcoming Juno gravity measurements and a dynamical inverse model
• pizza: An open-source pseudo-spectral code for spherical quasi-geostrophic convection
• Investigating Barotropic Zonal Flow in Jupiter's Deep Atmosphere using Juno Gravitational Data
• Lorentz force mediation of turbulent dynamo transitions
• Direct driving of simulated planetary jets by upscale energy transfer
• Reversal and amplification of zonal flows by boundary enforced thermal wind
• Rigorous bounds on the heat transport of rotating convection with Ekman pumping
• Validity of Sound-Proof Approaches in Rapidly-Rotating Compressible Convection: Marginal Stability vs. Turbulence
• The rotational influence on solar convection
• Assessing the validity of the anelastic and Boussinesq approximations to model solar inertial modes
• The effect of magnetic field on mean flow generation by rotating two-dimensional convection