Density Waves and the Viscous Overstability in Saturn's Rings

TL;DR

This study models the interaction between density waves and viscous overstability in Saturn's rings, revealing complex wave interactions and their effects on wave damping through hydrodynamical simulations and stability analysis.

Contribution

It introduces the first large-scale hydrodynamical model capturing the coexistence and interaction of density waves and viscous overstability in planetary rings.

Findings

Viscous overstability can dampen density waves depending on wave magnitudes.

Density waves can suppress viscous overstability under certain conditions.

Hydrodynamical simulations and stability analysis support the complex wave interactions.

Abstract

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.