Stylized Zelda VFX

Any idea what the texture itself would look like? I have some idea how alpha erosions work (basically uses a subtract node with a parameter) but im not sure what the actual ring texture itself would look like. Also notice how at the beginning there is no erosion and as it goes to the end of the lifetime the erosion takes effect.

I also notice a bit of panning cloud sort of look from this one:
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