Most of us have heard about the hexagon pattern seen in polar jet flow on Saturn. In doing a lot of different views of the Earth on Nullschool, I’ve managed to catch a picture of a sort of a hexagon on Earth. Right now the same view looks more like a square, so it does change over time, at least for Earth.
IMHO, this is an artifact of the projection where curvature of the jet around cyclones gets made into straight lines in the projection. But that just suggests that perhaps the same thing could be happening with the Saturn polar projection and that “hexagon”. What does it look like when put into an equatorial projection, eh?
Unlike Saturn, this hexagon is showing up in the far polar pattern while the near polar jet looks very ‘loopy’. IMHO this is a clue as to the degree of ‘loopy’ and nature of the projection needed to make a hexagon out of curving flow. Also, the Earth pattern is more irregular, likely, IMHO, due to the effect of land forms and our more shallow atmosphere layer.
Unfortunately, I don’t have an equatorial projection from exactly that same day ( I thought I saved one, and it might be buried somewhere, but is not to hand at the moment). Here is one from a nearby date, and, as I recall, things were not that different between the two dates.
Note the tendency for similar sized cyclonic air patterns spacing at similar distances from each other around the South Pole. That in my opinion is what is happening on Saturn, but deep enough that it has regularized by the time it is above the cloud level and much more stable in a gas giant.
In summary, I don’t think this is an answer, but I think it points in the direction of one. When the various heat moving cyclones cozy up to a pole, they close pack into a set of six. These, then, curve the air flow around them. At some strength and distance from the pole, the polar projection straightens out those curves into a hexagon. But in the real world it’s wavy in a projection from the side. IMHO a natural consequence of heat flow leading to minimal energy systems dumping heat to the poles. Likely to show up whenever the heat balance is in a particular range that makes that many cyclones that close to the pole.
Or perhaps this was just a lucky catch of an optical illusion ;-) But a pretty one…