Cheap solution: Take a torus. Scale it way up, like 2000% Parent it to some other simple thing like a box, off-center as seen here. Expand the x-scale of the box so that it stretches out the torus. Apply a Noise node to the transparency (and maybe also the color) of the torus. Then you can animate the Y-rot of the torus to get a steady, straight-looking flow along most of the scene.

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