On the Formation of the Fine-Scale Structure in Saturn's B Ring

Schmit, U.; Tscharnuter, W. M.

doi:10.1006/icar.1999.6078

Cited by 43 publications

(53 citation statements)

References 25 publications

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“…1. This was also found in a numerical solution of the nonlinear isothermal hydrodynamic equations far from threshold β = β cr (k) performed by Schmit and Tscharnuter (1999).…”

Section: Eigensolutionssupporting

confidence: 69%

“…The saturation sets in first for the fastest growing wavelength and then gradually for those that grow more slowly and is characterized by an interaction of modes of different wavelengths. In a large system this interaction could lead to the formation of a superimposed modulation of the saturated amplitude of oscillation on a much longer length-scale as the wavelength of maximal growth rate (Schmit and Tscharnuter 1999), resembling the structure actually seen in the B-ring.…”

Section: Implications For Saturn's Ringsmentioning

confidence: 86%

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Viscous Overstability in Saturn's B-Ring II. Hydrodynamic Theory and Comparison to Simulations

Schmidt¹

2001

Icarus

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We investigate the viscous oscillatory instability (overstability) of an unperturbed dense planetary ring, an instability that might play a role in the formation of radial structure in Saturn's B-ring. We generalize existing hydrodynamic models by including the heat flow equation in the analysis and compare our results to the development of overstable modes in local particle simulations. With the heat flow, in addition to the balance equations for mass and momentum, we take into account the balance law for the energy of the random motion; i.e., we allow for a thermal mode in a stability analysis of the stationary Keplerian flow. We also incorporate the effects of nonlocal transport of momentum and energy on the stability of the ring. In a companion paper (Salo, H., J. Schmidt, and F. Spahn 2001. Icarus, doi:10.1006/icar.2001.6680) we describe the determination of the local and nonlocal parts of the viscosity, the heat conductivity, the pressure, as well as the collisional cooling, together with their dependences on temperature and density, in local event-driven simulations of a planetary ring. The ring's self-gravity is taken into account in these simulations by an enhancement of the frequency of vertical oscillations z > . We use these values as parameters in our hydrodynamic model for the comparison to overstability in simulated rings of meter-sized inelastic particles of large optical depth with z / = 3.6. We find that the inclusion of the energy-balance equation has a stabilizing influence on the overstable modes, shifting the stability boundary to higher optical depths, and moderating the growth rates of the instability, as compared to a purely isothermal treatment. The non-isothermal model predicts correctly the growth rates and oscillation frequencies of overstable modes in the simulations, as well as the phase shifts and relative amplitudes of the perturbations in density and radial and tangential velocity.

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“…1. This was also found in a numerical solution of the nonlinear isothermal hydrodynamic equations far from threshold β = β cr (k) performed by Schmit and Tscharnuter (1999).…”

Section: Eigensolutionssupporting

confidence: 69%

Section: Implications For Saturn's Ringsmentioning

confidence: 86%

Viscous Overstability in Saturn's B-Ring II. Hydrodynamic Theory and Comparison to Simulations

Schmidt¹

2001

Icarus

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“…Note the changing perspective over the 13-h period, as the spacecraft flew nearly directly over the South Pole. Goertz & Morfill 1988;Schmit & Tscharnuter 1999;Tremaine 2003) or ballistic transport (Durisen et al 1989;Durisen 1995).…”

Section: Ringsmentioning

confidence: 99%

Observations in the Saturn system during approach and orbital insertion, with Cassini's visual and infrared mapping spectrometer (VIMS)

Brown¹,

Baines

Bellucci³

et al. 2006

A&A

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The Visual and Infrared Mapping Spectrometer observed Phoebe, Iapetus, Titan and Saturn's rings during Cassini's approach and orbital insertion. Phoebe's surface contains water ice, CO 2 , and ferrous iron. Iapetus contains CO 2 and organic materials. Titan's atmosphere shows methane fluorescence, and night-side atmospheric emission that may be CO 2 and CH 3 D. As determined from cloud motions, the winds at altitude 25-30 km in the south polar region of Titan appear to be moving in a prograde direction at velocity ∼1 m s −1 . Circular albedo features on Titan's surface, seen at 2.02 µm, may be palimpsests remaining from the rheological adjustment of ancient impact craters. As such, their long-term persistence is of special interest in view of the expected precipitation of liquids and solids from the atmosphere. Saturn's rings have changed little in their radial structure since the Voyager flybys in the early 1980s. Spectral absorption bands tentatively attributed to Fe 2+ suggest that iron-bearing silicates are a source of contamination of the C ring and the Cassini Division.

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“…In the following section we give a brief account of the stability analyses of a thin granular disk in terms of the diffusion instability, also called viscous instability in the literature ( [25,24,45]), and viscous overstability ( [36,37,33,35,34]). …”

Section: Stability Of Dense Ringsmentioning

confidence: 99%

“…This lack of an explanation in terms of external perturbations 3 stimulated the search for mechanisms of intrinsic instability, that could produce at least part of the observed structure. Prominent models proposed in the literature are the diffusion instability [25,24,45], ballistic transport models [11,13,9,12], transport related to electromagnetic effects on small grains [17,16,38], viscous overstability [36,37,33,35], or instability of the radial shear profile due to a certain dependence of shear stress on the shear rate of the flow [43].…”

Section: Stability Of Dense Ringsmentioning

confidence: 99%

Hydrodynamic Description of Planetary Rings

Spahn

Schmidt

2006

GAMM-Mitteilungen

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We demonstrate the suitability of a hydrodynamic description of the dynamics of a dense planetary ring considering as an example the viscous oscillatory instability. For the successful application of hydrodynamics the transport coefficients must be known as functions of surface mass density σ and the granular temperature T of the ring material. We arrange scaling laws for these quantities and use parameters determined from particle simulations of a planetary ring. With such a preparation, the theory predicts an oscillatory instability of a dense ring: waves of radial wavelengths λ ≈ 100m...200m evolve, driven by the combined effects of viscous momentum flux and Coriolis force. These predictions are confirmed by direct particle simulations: wavelengths of the unstable modes, their growth rates, as well as the properties of the eigenfunctions of the perturbations. This success bears the hope to explain a class of so-called fine-structure in Saturn's rings, which are poorly understood to date. The experiments of the Cassini-spacecraft in orbit around Saturn offer the unique chance to identify the predicted density features by analyzing the imaging and occultation data.

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On the Formation of the Fine-Scale Structure in Saturn's B Ring

Cited by 43 publications

References 25 publications

Viscous Overstability in Saturn's B-Ring II. Hydrodynamic Theory and Comparison to Simulations

Viscous Overstability in Saturn's B-Ring II. Hydrodynamic Theory and Comparison to Simulations

Observations in the Saturn system during approach and orbital insertion, with Cassini's visual and infrared mapping spectrometer (VIMS)

Hydrodynamic Description of Planetary Rings

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