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Large-scale N-body simulations of the viscous overstability in Saturn's rings

We present results from large-scale particle simulations of the viscous overstability in Saturn's rings. The overstability generates a variety of structure on scales covering a few hundred metres to several kilometres, including axisymmetric wavetrains and larger-scale modulations. Such patterns have been observed in Saturn's rings by the Cassini spacecraft. Our simulations model the collisional evolution of particles in a co-rotating patch of the disk. These are the largest N-body simulations of the viscous overstability yet performed. The radial box size is five orders of magnitude larger than a typical particle radius, and so describes a 20-50 km radial portion of the rings. Its evolution is tracked for more than 10,000 orbits. In agreement with hydrodynamics, our N-body simulations reveal that the viscous overstability exhibits a rich set of dynamics characterised by nonlinear travelling waves with wavelengths of a few hundred meters. In addition, wave defects, such as sources and shocks, punctuate this bed of waves and break them up into large-scale divisions of radial width ~5 km. We find that the wavelength of the travelling waves is positively correlated with the mean optical depth. In order to assess the role of the numerical boundary conditions and also background ring structure, we include simulations of broad spreading rings and simulations with a gradient in the background surface density. Overall, our numerical results and approach provide a tool with which to interpret Cassini occultation observations of microstructure in Saturn's rings. We present an example of such a synthetic occultation observation and discuss what features to expect. We also make the entire source code freely available.