Using a modified N-body code to include periodic boundary conditions in a perturbed shear flow, we investigate the role of viscosity on the dynamics of perturbed rings with optical depth tau similar to 1. In particular, we are concerned with rings such that q = a(de/da) not equal 0, where a is the semi-major axis and e is the eccentricity. We confirm the possibility that, for a sufficiently perturbed ring, the angular momentum luminosity may reverse direction with respect to the unperturbed ring (Borderies, N., P. Goldreich, and S. Tremaine 1983a. Icarus 55, 124-132). We use observationally constrained parameters for the delta and epsilon uranian rings, as well as the outer portion of Saturn's B ring. We find that understanding the effects of viscosity for the uranian rings requires that both local and non-local transport terms be considered if the coefficient of restitution experimentally obtained by Bridges et al. (Bridges, F. G., A. Hatzes, and D. N. C. Lin 1984. Nature 309, 333-335.) is appropriate for ring particles. We also find evidence that the criterion for viscous overstability is satisfied in the case of high optical depth rings, as originally proposed by Borderies et al. (Borderies, N., P. Goldreich, and S. Tremaine 1985. Icarus 63, 406-420.), making viscous overstability a leading candidate mechanism to explain the non-axisymmetric structure present in the outer portion of Saturn's B ring. To better understand our patch-code results eve extend a non-local and incompressible fluid model used by Borderies et al. for dense rings. We incorporate local and nonlocal transport terms as well as compressibility, while retaining the same number of arbitrary model parameters. (C) 1996 Academic Press, Inc.
