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G.R. Stewart, K. Ohtsuki (Univ. of Colorado)
Local N-body simulations of the outer portions of Saturn's rings display the cyclical growth and decay of elongated clumps of ring particles. The radial wavelength of these clumps is roughly given by Toomre's theory for axisymmetric instabilities in self-gravitating fluid disks. The purpose of this work is to develop a theory that predicts the azimuthal wavelength of the clumps. The azimuthal wavelenghth is important for describing the pitch angle of the clumps and hence the magnitude of the azimuthal brightness variations that are observed in Saturn's rings. As a first step toward this goal, we simulated the evolution an isolated narrow ring using the local N-body technique. We find that the ring first collapses to a dense narrow ring where the particles are closely packed. Within half of an orbit period, the narrow ring develops wavy edges while maintaining a nearly constant density. The azimuthal wavenumber of this instability appears to be determined by a balance between pressure forces and self-gravity on the edges of the collapsed ring and can therefore be explained by a variation of the Papaloizou-Pringle instability. By 3/4 of an orbit period, the entire ring has begun to separate azimuthally into clumps which rapidly shear out into elongated structures. The gravitational interactions between these structures causes radial spreading of the ring particles and hence a large effective viscosity. The viscosity of Saturn's A ring may be dominated by a similar mechanism.