Do we know why ie Saturn rings are not spiral-like? Ie due to their age (some relatively recently broken down comets) or some other forces that keep them spread evenly? Or just gravity is too weak amongst them for those smaller pieces of rock
Moons close to the rings tend to keep the particles of the ring confined within a narrow band (which is why they are called "shepherd moons").
Just trying to understand what you're getting at here. About what axis would you expect them to spiral? From normal mechanics + gravity I would expect them to orbit more or less elliptically about the polar axis of Saturn rather than spiral, but I don't know much about astrophysics.