A Quasigeostrophic Model of Zonal Wind Generation on the Gas Giants

Abstract:

Convecting fluids under rapid rotation play an important role in many geophysical systems. In such such systems, the dominant force balance is geostrophic, between the Coriolis term and the pressure gradient, and the resulting motion exhibits strongly 2D columnar structures which are mostly invariant parallel to the axis of rotation. To exploit this rigidity, quasigeostrophic (QG) models of convection have been developed by integrating the equations of motion in the axial direction, averaging over small departures from two dimensionality. Evolving these axially averaged 2D variables, rather than the full 3D variables, enables these models to reproduce the mean dynamics of the system at a lower computational cost, and hence more aggressive parameters than are accessible to direct 3D simulations can be explored. Traditionally, these QG models have only been devised for the region of a convection shell outside the tangent cylinder, which circumscribes the inner boundary of the convection shell. In the present work we have extended the QG framework to the region inside the tangent cylinder where axial convection, transporting heat from the inner to the outer boundary of the shell, is the dominant mode. Thus, in addition to the traditional QG equations, we must also solve the axial flow equation. Numerical results from our 2D QG model applied to a Jovian-like system of thermal convection in a thin spherical shell will be presented which demonstrate that it is capable of capturing the major features of the dynamics of such a system. In particular, our model successfully reproduces the atmospheric zonal jets produced by full 3D models and observed on the gas giant.