The Emergence of Zonal Jets in a New Anelastic Model of Rapidly Rotating Spherical Convection in Gas Giants

We study the emergence and evolution of large-scale zonal flows, as observed on the gas giant planets, using a newly developed 3-D GCM in spherical shell geometry. This new model is specified in terms of a grid-point based methodology which employs a hierarchy of tessellations derived from successive dyadic refinements of the spherical icosahedron. One major advantage of this multi-grid methodology is that it allows for nearly linear growth of complexity in operation count as opposed to the spectral transform models, which by their nature are at least quadratic in computational cost. Another potential advantage is the absence of pole problems, and therefore the ability of the code to capture important features of the dynamics in the polar regions. An added bonus of this new methodology is the possibility for greater local control over the computational mesh. The physical basis of the model is the anelastic approximation of the hydrodynamic equations of motion, continuity, and classical thermodynamics. We describe a comparative investigation of the convective response of a layer of Boussinesq fluid and density stratified fluid in rapidly rotating, three-dimensional spherical shell geometry subject to isothermal temperature boundary conditions. The physical scaling is determined by the 3 non-dimensional parameters: Ekman, Prandtl and Rayleigh numbers, while the depth of the shell is a variable parameter. We present results from long runs of the model in the Boussinesq and fully anelastic approximation for two different relative shell depths (10 % and 25 %) and compare the formation and evolution of zonal jets, which are driven by vigorous convection and strong Coriolis force. These test cases are of particular relevance to the outer layers of the gas giant planets where a number of open questions associated with the formation and evolution of coherent structures await solution. The numerical experiments are performed in the high Rayleigh number (≥ 106), low Ekman number (≤ 3 × 10-4) regime, with the Prandtl number fixed to unity. Mixed mechanical boundary conditions for velocity (free at the top and rigid at the bottom of the shell) are employed in both experiments. In these experiemnts Reynolds stresses are balanced only by weak viscous forces and drive strong eastward jets at low latitudes at the outer surface and weaker oscillatory jets at high latitudes as observed in the weather layer of the gas giant planets. In order to resolve the fine-grained structure of the zonal jets observed by the Galileo probe for Jupiter and most recently by the Cassini spacecraft for Saturn, very high spatial resolution will be required. A pronounced feature of our experiments is that we invariably observe strong convection developing inside the tangent cylinder where the effect of the Coriolis force is small, as opposed to the powerful zonal flows which develop outside the tangent cylinder. Clearly, simulations over a wider range of shell depths and more extreme values of the Rayleigh and Taylor numbers must be carried out to determine which spherical shell geometries and control parameter values best fit available equatorial jet observations. In addition, the effects of density stratification in the fully anelastic version of the code together with the proper mechanical boundary conditions for velocity deserve further study in order to better understand the mechanism whereby large scale zonal flows on the gas giant planets develop from strongly forced rapidly rotating convection.