This looks like m=2 swirling instability mode of the axisymmetric jet, but how could an axisymmetric jet form up in the sky like that?
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Helix clouds are quite uncommon - a Google search reveals only a few, oft repeated, images. There are several short discussions about them on various forums, the longest of which glances over a few interesting ideas including an attempt to quantify the evolution of a well-documented Muscovian example with time.
It isn't a jet stream core - they are too small (and found in areas where the jet stream isn't). You need something capable of generating a long thin cloud, and something to spin it. The first part is easy: a contrail being the prime example (as well as several other common cloud types). The second part requires some phenomenon to generate a twisting cylinder of air, and there is one! Strong localised vertical shear generates horizontal vortices that tend to twist over their length.
That covers a single helix cloud - but what about the double helices? Well, contrails from larger airplanes form a fine example of two distinct lines of cloud, which, under the scenario described in the previous paragraph would wrap around each other to form such a shape.
Example over Mauna Kea, generated from ambient cirrostratus.
Example over Moscow, almost certainly generated from a fleeting contrail.
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