  This paper addresses resonantly forced spiral density waves in a dense
planetary ring which is close to the threshold for viscous overstability. We
solve numerically the hydrodynamical equations for a dense, axisymmetric thin
disk in the vicinity of an inner Lindblad resonance with a perturbing
satellite. The spiral shape of a density wave is taken into account through a
suitable approximation of the advective terms arising from the fluid orbital
motion. This paper is a first attempt to model the co-existence of resonantly
forced density waves and short-scale axisymmetric overstable wavetrains in
Saturn's rings by conducting large-scale hydrodynamical integrations. These
integrations reveal that the two wave types undergo complex interactions, not
taken into account in existing models for the damping of density waves. In
particular it is found that, depending on the relative magnitude of both wave
types, the presence of viscous overstability can lead to a damping of an
unstable density wave and vice versa. The damping of viscous overstability by a
density wave is investigated further by employing a simplified model of an
axisymmetric ring perturbed by a nearby Lindblad resonance. A linear
hydrodynamic stability analysis as well as local N-body simulations of this
model system are performed and support the results of our large-scale
hydrodynamical integrations.
