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NASA has just shown a more detailed picture of the hexagonal vortex/storm on Saturn:

http://www.ibtimes.com/nasa-releases-images-saturns-hexagon-mega-storm-may-have-been-swirling-centuries-1496218
https://en.wikipedia.org/wiki/Saturn_hexagon

Is that theoretically understood what is the cause behind this eye-catching nontrivial, regular yet not circular, shape? If so, what is the cause? I expect some explanation in terms of "nonlinear equations" of "mathematical physics" and "solitons".

P.S. (added a day after this question and the first answer was posted): On my blog where I posted the same question, people came up with some articles and phrases like "Rossby waves" and "resonance of latitude-dependence Coriolis frequency".

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I don't think solitons are relevant for this phenomenon –  Christoph Dec 5 '13 at 14:34
    
Interesting, can you use the same method to create pentagons and octagons? –  Jitter Dec 5 '13 at 18:05
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I've already answered this question here, though I won't repost it as hdhondt already has addressed the issue with the same reference. –  Manishearth Dec 6 '13 at 6:10
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I doubt if anyone has come up with a complete explanation, but some laboratory simulations have created similar patterns. They happen if the central and surrounding areas in a flat, circular disk of fluid have different velocities. Emily Lakdawalla at The Planetary Society covers it at this site. She also explains how other patterns (triangles & heptagons) form under similar circumstances.

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Interesting, thanks. –  Luboš Motl Dec 5 '13 at 9:33
    
The full paper by Aguiar, Read, Wordsworth, Salter and Yamazaki is here: sciencedirect.com/science/article/pii/S0019103509004382 . It looks like they did a linear stability analysis of certain solutions of the barotropic vorticity equation en.wikipedia.org/wiki/Barotropic_vorticity_equation describing the flow in the atmosphere, which then motivated their experiments. –  j.c. Dec 5 '13 at 10:13
    
The experimental pictures are interesting - the hexagon arises because it's a circle being squeezed by 6 other potatoes around it. That could make sense as an approach to qualitatively explain the Z6 symmetry and why the solution is stable. –  Luboš Motl Dec 5 '13 at 10:40
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