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

Latter, Henrik N.; Ogilvie, Gordon I.

doi:10.1016/j.icarus.2009.03.011

Cited by 23 publications

(23 citation statements)

References 57 publications

(130 reference statements)

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“…Clear signatures of these features in a wavelet plot are presented in Appendix A for a simulation with a much longer domain. This configuration of dynamical elements reflects behaviour in the complex Ginzburg-Landau equation, which serves as a good reduced model for the overstable system (Aranson & Kramer 2002;Latter & Ogilvie 2009). It also reproduces qualitatively the hydrodynamical simulations of Latter & Ogilvie (2010), yet there exist interesting discrepancies.…”

Section: Fiducial Simulationmentioning

confidence: 89%

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

Rein¹,

Latter²

2013

Monthly Notices of the Royal Astronomical Society

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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 their 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 make the entire source code freely available.

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Section: Fiducial Simulationmentioning

confidence: 89%

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

Rein¹,

Latter²

2013

Monthly Notices of the Royal Astronomical Society

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“…However, additional theoretical and observational work is needed to validate or refute this interpretation. While established linear theories can provide information about the conditions required to initiate overstability, the non-linear processes responsible for determining the final amplitude and wavelength of the patterns are still not perfectly understood, especially for situations where the mutual selfgravity of the particles cannot be ignored (Schmit and Tscharnuter 1999;Salo et al 2001;Schmidt et al 2009;Latter and Ogilvie 2009;Rein and Latter 2013). Since we cannot compare our observations with detailed theoretical predictions for the behavior and distribution of overstabilities, we will instead discuss briefly two ways these measurements could help inform future theoretical work on overstable phenomena.…”

Section: Discussionmentioning

confidence: 99%

Exploring Overstabilities in Saturn's a Ring Using Two Stellar Occultations

Hedman

Nicholson

Salo

2014

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Certain regions of Saturn's rings exhibit periodic opacity variations with characteristic radial wavelengths of up to a few hundred meters that have been attributed to viscous overstabilities. The Visual and Infrared Mapping Spectrometer (VIMS) onboard the Cassini spacecraft observed two stellar occultations of the star γ Crucis that had sufficient resolution to discern a sub-set of these periodic patterns in a portion of the A ring between 124,000 and 125,000 km from Saturn center. These data reveal that the wavelengths and intensities of the patterns vary systematically across this region, but that these parameters are not strictly determined by the ring's average optical depth. Furthermore, our observations indicate that these opacity variations have an azimuthal coherence scale of around 3000 km.

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“…i.e. the solution is a traveling wave with constant growth (or decay) rate, determined by the imaginary part of ω (Schmit and Tscharnuter (1995); Schmidt et al (2001); Latter and Ogilvie (2009)). For q > 0, the behavior is more complicated.…”

Section: Viscous Overstability In a Perturbed Ring: Axisymmetric Apprmentioning

confidence: 99%

Density waves and the viscous overstability in Saturn’s rings

Lehmann

Schmidt

Salo

2019

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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 thin disk in the vicinity of an inner Lindblad resonance with a perturbing satellite. Our numerical scheme is one-dimensional so that 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 free overstable wavetrains as observed 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 the short-scale 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.

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

Cited by 23 publications

References 57 publications

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

Large-scale N-body simulations of the 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

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