The effect should be as similar as possible to this, though it does not need to be at planetary scale.
I was thinking that it could be done offline via particles, perhaps by directing their motion in some way. Then rendering the frames to a texture and playing these back in a loop for real-time rendering?
But I wonder if there is some other real-time way... maybe mesh patches shaped like swirls can be moved around, after being textured carefully, to imitate the motion of swirls of gaseous matter?