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Published March 15, 2025 | Published
Journal Article Open

Vortex crystals at Jupiter's poles: Emergence controlled by initial small-scale turbulence

  • 1. ROR icon California Institute of Technology
  • 2. ROR icon University of Michigan–Ann Arbor

Abstract

At the poles of Jupiter, cyclonic vortices are clustered together in patterns made up of equilateral triangles called vortex crystals. Such patterns are seen in laboratory flows but never before in a planetary atmosphere, where the planet’s rotation and gravity add new physics. Siegelman (2022b) used a one-layer quasi-geostrophic (QG) model with an infinite radius of deformation to study the emergence of vortex crystals from small-scale turbulence, and Li (2020) showed that shielding of the vortices is important for the stability of the vortex crystals. Here we use the shallow water (SW) equations at the pole of a rotating planet to study the emergence and evolution of vortices starting from an initial random pattern of small-scale turbulence. The flow is in a single layer with a free surface whose slope produces the horizontal pressure gradient force. With the planet’s radius and rotation used to define the units, only three input parameters are needed to define the system: the mean kinetic energy of the initial turbulence, the horizontal scale of the initial turbulence, and the radius of deformation of the undisturbed fluid layer. We identified a non-dimensional number, Δh/h, which is related to the relative layer thickness variation of the initial turbulence and determines whether the vortex crystal or chaotic patterns emerge: Small Δh/h values lead to vortex crystals, and large Δh/h values lead to chaotic patterns. The value Δh/h is related to the radius of deformation as L_d⁻². This means that a large polar radius of deformation is positively correlated to the emergence of vortex crystals, and this implies either a polar atmosphere enriched with water or deeper roots for the vortices than previously estimated.

Copyright and License

© 2024 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Acknowledgement

This research was carried out at the California Institute of Technology under a contract with the National Aeronautics and Space Administration (NASA), Grant /Cooperative Agreement Number 80NSSC 20K0555, and a contract with the Juno mission, which is administered for NASA by the Southwest Research Institute. CL was supported by the NASA Juno Program , under NASA Contract NNM06AA75C from the Marshall Space Flight Center, through subcontract 699056KC to the University of Michigan from the Southwest Research Institute. We also thank Dr. Huazhi Ge for his suggestions in developing the simulations presented in this paper.

Contributions

Sihe Chen: Writing – review & editing, Writing – original draft, Visualization, Software, Methodology, Formal analysis. Andrew P. Ingersoll: Writing – review & editing, Supervision, Funding acquisition, Conceptualization. Cheng Li: Writing – review & editing, Supervision, Software, Methodology, Investigation.

Data Availability

The model program is publicly available on GitHub under the repository https://github.com/chengcli/canoe. The simulation output data that support this study’s findings are available from the corresponding author upon reasonable request.

Supplemental Material

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Additional details

Created:
January 2, 2025
Modified:
January 2, 2025