Nonlinear Atmospheric Flow Patterns Confined to Zonal Cloud Bands

Abstract We derive, at leading order in the thin-shell parameter, a consistent set of nonlinear governing equations for the dynamics of flows confined to a zonal cloud band such as those on Jupiter, in a thin layer near the top of the planetary troposphere. Some exact solutions are provided in the material (Lagrangian) framework. The explicit specification of the individual particle paths enables a detailed study of these flows that model oscillations superimposed on a mean current. This approach is applied to Jupiter’s Great Red Spot and to the filamentary zonal flow at its southern boundary. Significance Statement We propose a new approach to the study of some flow patterns visible in zonal cloud bands on Jupiter. Motivated by observations showing that the dominant motions in the cloud bands on Jupiter are zonal and rotational, we provide some exact solutions to the governing equations for the leading-order dynamics. These solutions model rotating particle paths interacting with a straight-line flow. The approach offers detailed insight into basic features of the flow, highlighting the interplay between density variations and wind forcing. The exact solutions presented here are a useful starting point for a perturbation analysis. Current advances in computing methods enhance the feasibility of numerical simulations of perturbed flows that are designed to capture a wider range of effects, whose relevance can be ascertained by comparison with the exact solutions presented in this paper.