A hexagon is a boundary shape with the least energy. What you are really probably seeing is a circle that has pushed outwards against another set of forces and reached equilibrium (differing temperatures, gasses, who knows what). I have been playing with voronoi diagrams and diffusion limited aggregation recently , and it is amazing some of the structures that will emerge when a system reaches equilibrium. It is possible that certain forces have aligned with their peak energies in the form of a regular polyhedra, which happens all over nature on large and small scales.
Its "common knowledge" that standard twist drills sometimes cut stable polygons instead of perfect circles if its a wimpy metal for the drill and a tough metal for the work (which is why woodworkers don't see this often). Thats why machinists rough cut a hole with a standard twist drill about 1/32 small then ream to precise diameter. Take something wiggly-ish thats X units long and it'll tend to catch in a corner, then sweep out a radius of X units until it slips free (and typically gets stuck in the next corner). Unfortunately this is stable and self reinforcing. Hexagons and higher order polygons are pretty rare usually you get somewhat oversize triangle-ish shaped hole. Yes the sides are not precisely flat they are curved.
So the above is a factual statement of reality. A wild conjecture is this metalworking effect might be a physical manifestation of what the OP is talking theoretically about. A further (pair of?) wild conjecture is either my example or the OPs example could have something to do with saturn's hexagon. I would not be completely surprised if there is a numerological oscillation set up where 1/6th (or 1/3rd) of a planetary rotation is exactly long enough for prevailing winds or a sonic boom or something like that to cross the diameter of the hexagon. Or we're seeing a weird phase change trick as "something" evaporates and condenses in response to a rolling atmospheric high pressure zone.
There's also a circle packing argument where at a deeper atmospheric layer than we can see, there's six rotating vortexes which just fit within the hex.
All I can say is I'm thankful its a stable 6-agon instead of a stable 5-agon or we'd never hear the end of it from the nutcases.
There are a number of fluid dynamic studies that show 'angled' flow, generally around mixed densities and viscositys coming into contact with each other. That said, its a cool effect.
If it were science fiction there would be a giant hexagonal shaped structure under the clouds on the pole. Waiting ...
>It turned out that the rate of ring rotation changed the shape of the pattern from a circle to just about anything, including ovals, triangles, squares and various polygons.
Wow. Imagine if it were a square on Saturn. I think that would provide more fodder for sci fi writers than the hexagon.
http://www.bioedonline.org/news/news.cfm?art=2531Researchers at the Technical University of Denmark in Lyngby have created similar geometric shapes (holes in the form of stars, squares, pentagons and hexagons) in whirlpools of water in a cylindrical bucket.
The link mentions "Saturn's South Pole … with its rotating vortex" with a link to another post from the website with a picture of the vortex, but the description is that of "the north pole of Saturn… [a] vortex of strange and complex swirling clouds" encompassed in a hexagon.
Reminds me of the 1986 novel Saturnalia - http://en.wikipedia.org/wiki/Saturnalia_(Callin_novel) - in which the aliens who leave calling cards in the moons of Saturn are called "hexies" because they use so many 6's in their messages.
http://www.popsci.com/science/article/2010-04/saturns-myster...