Continuation and Damping of Zonal Flows by Stably Stratified layers

Geostrophic zonal flows appear naturally in rapidly rotating, convective systems that resemble the convective atmospheres of giant planets. However, the depth of the flows is potentially limited by stratified layers inhibiting convection. Here we study the continuation and damping of zonal flows across the interface and into such a stratified layer. In order to analyse the problem in a systematic way, we validate cartesian and analytical models by using spherical shell models with enforced axisymmetry. Compared to full 3D models they provide the advantage of being much less computationally demanding and producing plentiful jets within the shell's tangent cylinder.

The analytical model predicts that for weaker stratification, the damping of the jets in the stable layer follows the prediction of the classic linear theory of penetrative convection and thus scales with the length scale of the jets and the relative stratification ($N/\Omega$, where $N$ is the Brunt-V\"{a}is\"{a}l\"{a} frequency and $\Omega$ the rotation rate). However, for strong stratifications, characteristic for compositional gradients (eg. He-rain), the damping rate becomes independent of $N/\Omega$ and is solely controlled by the jet width. The axisymmetric spherical shell simulations verify this prediction over a wide range of parameters. These results yield also important consequences for modelling the wind-induced gravity field anomalies of Gas Giants.