Hydrodynamical simulations of viscous overstability in Saturn's rings

TL;DR

This study uses hydrodynamical simulations to explore the nonlinear behavior of viscous overstability in Saturn's rings, revealing the formation of nonlinear wavetrains and their potential link to observed microstructures.

Contribution

It provides the first detailed nonlinear hydrodynamical modeling of viscous overstability in planetary rings, connecting simulations with Cassini observations.

Findings

Nonlinear wavetrains dominate the simulated microstructures.

Waves exhibit small chaotic fluctuations and wave defects.

Boundary conditions significantly influence long-term behavior.

Abstract

We perform axisymmetric hydrodynamical simulations that describe the nonlinear outcome of the viscous overstability in dense planetary rings. These simulations are particularly relevant for Cassini observations of fine-scale structure in Saturn's A and B-ring, which take the form of periodic microstructure on the 0.1 km scale, and irregular larger-scale structure on 1-10 km. Nonlinear wavetrains dominate all the simulations, and we associate them with the observed periodic microstructure. The waves can undergo small chaotic fluctuations in their phase and amplitude, and may be punctuated by more formidable `wave defects' distributed on longer scales. It is unclear, however, whether the defects are connected to the irregular larger-scale variations observed by Cassini. The long-term behaviour of the simulations is dominated by the imposed boundary conditions, and more generally by the limitations of the local model we use: the shearing box. When periodic boundary conditions are imposed, the system eventually settles on a uniform travelling wave of a predictable wavelength, while reflecting boundaries, and boundaries with buffer zones, maintain a disordered state. The simulations omit self-gravity, though we examine its influence in future work.