On the origin of irregular structure in Saturn’s rings

We suggest that the irregular structure in Saturn’s B ring arises from the formation of shear-free ring-particle assemblies of up to ∼ 100 km in radial extent. The characteristic scale of the irregular structure is set by the competition between tidal forces and the yield stress of these assemblies; the required tensile strength of ∼ 10 dyn cm is consistent with the sticking forces observed in laboratory simulations of frosted ice particles. These assemblies could be the nonlinear outcome of a linear instability that occurs in a rotating fluid disk in which the shear stress is a decreasing function of the shear. We show that a simple model of an incompressible, non-Newtonian fluid in shear flow leads to the Cahn-Hilliard equation, which is widely used to model the formation of structure in binary alloys and other systems. Subject headings: planets: rings — celestial mechanics