Why is there billowing dust in nebulae? Why do some nebulae look like the billowing clouds? Wouldn't that require something like a viscosity in empty space?
This is a very complex answer. It has to do a lot with gravity and electromagnetism. Nebulae are made of particles that act according to those forces and give you the illusion of viscosity. Those particles are actually moving. Take a look at this simulation it might give you an idea: Simulation