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Nonlinear Atmospheric Flow Patterns Confined to Zonal Cloud Bands: Saturn’s Hexagon

Lookup NU author(s): Professor Robin Johnson

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Abstract

© 2025 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license.Motivated by Saturn’s circumpolar hexagonal wave, 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 thin layer in a narrow, zonal, cloud band on Saturn and driven by internal heat forcing. Some exact solutions of this nonlinear system are derived in the Lagrangian setting. These solutions describe oscillations superimposed on a sheared high-speed zonal jet, with hypotrochoidal particle trajectories in the shape of a regular polygon with rounded corners. We show that the specificnumberofcornersis determined by the heat forcing and by the location of the hexagonal pattern. The speeds and the temperature associated with this model for Saturn’s hexagon are in good agreement with observations.

Publication metadata

Author(s): Constantin A, Johnson RS

Publication type: Article

Publication status: Published

Journal: Journal of the Atmospheric Sciences

Year: 2025

Volume: 82

Issue: 9

Pages: 1815-1832

Print publication date: 01/09/2025

Online publication date: 20/08/2025

Acceptance date: 09/06/2025

ISSN (print): 0022-4928

ISSN (electronic): 1520-0469

Publisher: American Meteorological Society

URL: https://doi.org/10.1175/JAS-D-24-0260.1

DOI: 10.1175/JAS-D-24-0260.1

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