The viscous overstability, nonlinear wavetrains, and finescale structure in dense planetary rings

Abstract

This paper addresses the fine-scale axisymmetric structure exhibited in Saturn's A and B-rings. We aim to explain both the periodic microstructure on 150-220m, revealed by the Cassini UVIS and RSS instruments, and the irregular variations in brightness on 1-10km, reported by the Cassini ISS. We propose that the former structures correspond to the peaks and troughs of the nonlinear wavetrains that form naturally in a viscously overstable disk. The latter variations on longer scales may correspond to modulations and defects in the wavetrains' amplitudes and wavelength. We explore these ideas using a simple hydrodynamical model which captures the correct qualitative behaviour of a disk of inelastically colliding particles, while also permitting us to make progress with analytic and semi-analytic techniques. Specifically, we calculate a family of travelling nonlinear density waves and determine their stability properties. Detailed numerical simulations that confirm our basic results will appear in a following paper.

52 pages, 8 figures. Accepted in Icarus

References in corpus (5)

• Visualizing the geometry of state space in plane Couette flow
• Viscous overstability and eccentricity evolution in three-dimensional gaseous discs
• The linear stability of dilute particulate rings
• Dense planetary rings and the viscous overstability
• Properties and stability of freely propagating nonlinear density waves in accretion disks

Cited by in corpus (13)

• Long-term & large-scale viscous evolution of dense planetary rings
• Local and global dynamics of eccentric astrophysical discs
• Large-scale N-body simulations of the viscous overstability in Saturn's rings
• Hydrodynamical simulations of viscous overstability in Saturn's rings
• Exploring overstabilities in Saturn's A ring using two stellar occultations
• Density Waves and the Viscous Overstability in Saturn's Rings
• Viscous Overstability in Saturn's Rings: Influence of Collective Self-gravity
• The gravitational instability of a stream of co-orbital particles
• The ballistic transport instability in Saturn's rings II: nonlinear wave dynamics
• A Weakly Nonlinear Model for the Damping of Resonantly Forced Density Waves in Dense Planetary Rings
• The ballistic transport instability in Saturn's rings III: numerical simulations
• Filament formation due to diffusive instabilities in dusty protoplanetary disks
• The stress-pressure lag in MRI turbulence and its implications for thermal instability in accretion discs