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Hydrodynamics of Saturn’s Dense Rings

Published online by Cambridge University Press:  18 July 2011

M. Seiß  and
F. Spahn
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Abstract

The space missions Voyager and Cassini together with earthbound observations revealed a wealth of structures in Saturn’s rings. There are, for example, waves being excited at ring positions which are in orbital resonance with Saturn’s moons. Other structures can be assigned to embedded moons like empty gaps, moon induced wakes or S-shaped propeller features. Furthermore, irregular radial structures are observed in the range from 10 meters until kilometers. Here some of these structures will be discussed in the frame of hydrodynamical modeling of Saturn’s dense rings. For this purpose we will characterize the physical properties of the ring particle ensemble by mean field quantities and point to the special behavior of the transport coefficients. We show that unperturbed rings can become unstable and how diffusion acts in the rings. Additionally, the alternative streamline formalism is introduced to describe perturbed regions of dense rings with applications to the wake damping and the dispersion relation of the density waves.

Keywords

granular gasinstabilitieshydrodynamicsplanetary rings
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 4: Granular hydrodynamics , 2011 , pp. 191 - 218
Copyright
© EDP Sciences, 2011

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References

Albers, N., Spahn, F.. The influence of particle adhesion on the stability of agglomerates in Saturn’s rings. Icarus, 181 (2006), 292–301. CrossRefGoogle Scholar
Andrews, J. P.. Theory of Collision of Spheres of Soft Metals. Phil.Mag.S.7, 9 (1930), 58, 593–610. CrossRefGoogle Scholar
Araki, S., Tremaine, S.. The dynamics of dense particle disks. Icarus, 65 (1986), 83–109. CrossRefGoogle Scholar
Barbara, J. M., Esposito, L. W.. Moonlet Collisions and the Effects of Tidally Modified Accretion in Saturn’s F Ring. Icarus, 160 (2002), 1, 161–171. CrossRefGoogle Scholar
Borderies, N.. Ring dynamics. Celestial Mechanics and Dynamical Astronomy, 46 (1989), 207–230. CrossRefGoogle Scholar
Borderies, N., Goldreich, P., Tremaine, S.. Sharp edges of planetary rings. Nature, 299 (1982), 209–211. CrossRefGoogle Scholar
N. Borderies, P. Goldreich, S. Tremaine. Unsolved problems in planetary ring dynamics. In Planetary Rings (1984) pages 713–734.
Borderies, N., Goldreich, P., Tremaine, S.. A granular flow model for dense planetary rings. Icarus, 63 (1985), 406–420. CrossRefGoogle Scholar
Borderies, N., Goldreich, P., Tremaine, S.. Nonlinear density waves in planetary rings. Icarus, 68 (1986), 522–533. CrossRefGoogle Scholar
Borderies, N., Goldreich, P., Tremaine, S.. The formation of sharp edges in planetary rings by nearby satellites. Icarus, 80 (1989), 344–360. CrossRefGoogle Scholar
Brey, J. J., Dufty, J. W., Kim, C. S., Santos, A.. Hydrodynamics for granular flow at low density. Physical Review E, 58 (1998), 4638–4653. CrossRefGoogle Scholar
Bridges, F. G., Hatzes, A., Lin, D. N. C.. Structure, stability and evolution of Saturn’s rings. Nature, 309 (1984), 333–335. CrossRefGoogle Scholar
Brilliantov, N., Spahn, F., Hertzsch, J.-M., Pöschel, T.. Model for collisions in granular gases. Physical Review E, 53 (1996), 5382–5392. CrossRefGoogle ScholarPubMed
Brilliantov, N. V., Albers, N., Spahn, F., Pöschel, T, Collision dynamics of granular particles with adhesion. Phys. Rev. E, 76 (2008), 051302. Google Scholar
Canup, R. M., Esposito, L. W.. Accretion in the Roche zone: Coexistence of rings and ring moons. Icarus, 113 (1995), 331–352. Google Scholar
Charnoz, S., Salmon, J., Crida, A.. The recent formation of Saturn’s moonlets from viscous spreading of the main rings. Nature, 465 (2010), 752–754. CrossRefGoogle ScholarPubMed
Colwell, J. E., Cooney, J. H., Esposito, L. W., Sremčević, M.. Density waves in Cassini UVIS stellar occultations. 1. The Cassini Division. Icarus, 200 (2009), 574–580. CrossRefGoogle Scholar
Colwell, J. E., Esposito, L. W., Sremčević, M.. Self-gravity wakes in Saturn’s A ring measured by stellar occultations from Cassini. Geophysical Research Letters, 33 (2006), 7201. CrossRefGoogle Scholar
Colwell, J. E., Esposito, L. W., Sremčević, M., Stewart, G. R., McClintock, W. E.. Self-gravity wakes and radial structure of Saturn’s B ring. Icarus, 190 (2007), 127–144. CrossRefGoogle Scholar
J. N. Cuzzi, J. J. Lissauer, L. W. Esposito, J. B. Holberg, E. A. Marouf, G. L. Tyler, A. Boischot. Saturn’s Rings: Properties and Processes. In Planetary rings (R. Greenberg, A. Brahic, editors), pages 73–199, The University of Arizona Press 1984.
Cuzzi, J. N., Scargle, J. D.. Wavy edges suggest moonlet in Encke’s gap. Astrophysical Journal, 292 (1985), 276–290. CrossRefGoogle Scholar
Daisaka, H., Tanaka, H., Ida, S.. Viscosity in a Dense Planetary Ring with Self-Gravitating Particles. Icarus, 154 (2001), 296–312. CrossRefGoogle Scholar
Davis, D. R., Weidenschilling, S. J., Chapman, C. R., Greenberg, R.. Saturn ring particles as dynamic ephemeral bodies. Science, 224 (1984), 744–747. CrossRefGoogle ScholarPubMed
Dermott, S. F., Murray, C. D.. The dynamics of tadpole and horseshoe orbits. I - Theory. II - The coorbital satellites of Saturn. Icarus, 48 (1981), 1–22. CrossRefGoogle Scholar
Dermott, S. F., Murray, C. D., Sinclair, A. T.. The narrow rings of Jupiter, Saturn and Uranus. Nature, 284 (1980), 309–313. CrossRefGoogle Scholar
Esposito, L. W., Ocallaghan, M., West, R. A.. The structure of Saturn’s rings - Implications from the Voyager stellar occultation. Icarus, 56 (1983), 439–452. CrossRefGoogle Scholar
French, R. G., Nicholson, P. D.. Saturn’s Rings II. Particle sizes inferred from stellar occultation data. Icarus, 145 (2000), 502–523. CrossRefGoogle Scholar
Goldreich, P., Tremaine, S.. The excitation and evolution of density waves. Astrophysical Journal, 222 (1978), 850–858. CrossRefGoogle Scholar
Goldreich, P., Tremaine, S. D.. The velocity dispersion in Saturn’s rings. Icarus, 34 (1978), 227–239. CrossRefGoogle Scholar
Hatzes, A., Bridges, F. G., Lin, D. N. C.. Collisional properties of ice spheres at low impact velocities. Mon. Not. R. Astr. Soc., 231 (1988), 1091–1115. CrossRefGoogle Scholar
Hedman, M. M., Nicholson, P. D., Salo, H., Wallis, B. D., Buratti, B. J., Baines, K. H., Brown, R. H., Clark, R. N.. Self-Gravity Wake Structures in Saturn’s A Ring Revealed by Cassini VIMS. Astronomical Journal, 133 (2007), 2624–2629. CrossRefGoogle Scholar
Heißelmann, D., Blum, J., Fraser, H. J., Wolling, K.. Microgravity experiments on the collisional behavior of saturnian ring particles. Icarus, 206 (2010), 424–430. CrossRefGoogle Scholar
Henon, M.. A simple model of Saturn’s rings. Nature, 293 (1981), 33–35. CrossRefGoogle Scholar
Hertzsch, J.-M., Scholl, H., Spahn, F., Katzorke, I.. Simulation of collisions in planetary rings. Astronomy and Astrophysics, 320 (1997), 319–324. Google Scholar
Jenkins, J., Richman, M.. Grad’s 13-moment system for a dense gas of inelastic spheres. Arch. Ration. Mech. Anal., 87 (1985), 355–377. CrossRefGoogle Scholar
Latter, H. N., Ogilvie, G. I.. The linear stability of dilute particulate rings. Icarus, 184 (2006), 498–516. CrossRefGoogle Scholar
Latter, H. N., Ogilvie, G. I.. Dense planetary rings and the viscous overstability. Icarus, 195 (2008), 725–751. CrossRefGoogle Scholar
Latter, H. N., Ogilvie, G. I.. The viscous overstability, nonlinear wavetrains, and finescale structure in dense planetary rings. Icarus, 202 (2009), 565–583. CrossRefGoogle Scholar
Latter, H. N., Ogilvie, G. I.. Hydrodynamical simulations of viscous overstability in Saturn’s rings. Icarus, 210 (2010), 318–329. CrossRefGoogle Scholar
Lewis, M. C., Stewart, G. R.. Collisional Dynamics of Perturbed Planetary Rings. I. Astronomical Journal, 120 (2000), 3295–3310. CrossRefGoogle Scholar
Lin, D. N. C., Bodenheimer, P.. On the stability of Saturn’s rings. Astrophysical Journal, 248 (1981), L83–L86. CrossRefGoogle Scholar
Lin, D. N. C., Pringle, J. E.. A viscosity prescription for a self-gravitating accretion disc. Monthly Notices Royal Astron. Soc., 225 (1987), 607–613. CrossRefGoogle Scholar
Lissauer, J. J., Shu, F. H., Cuzzi, J. N.. Moonlets in Saturn’s rings. Nature, 292 (1981), 707–711. CrossRefGoogle Scholar
Longaretti, P.-Y.. Saturn’s main ring particle size distribution - an analytic approach. Icarus, 81 (1989), 51–73. CrossRefGoogle Scholar
Lynden-Bell, D., Pringle, J.. The evolution of viscous discs and the origin of the nebular variables. Mon.Not.Roy.Astron.Soc, 168 (1974), 603–637. CrossRefGoogle Scholar
Petit, J.-M., Henon, M.. A numerical simulation of planetary rings. III - Mass segregation, ring confinement, and gap formation. Astronomy and Astrophysics, 199 (1988), 343–356. Google Scholar
C. C. Porco. S/2005 S 1. IAU Circ., 8524 (2005), 1.
Pringle, J. E.. Accretion discs in astrophysics. Ann. Rev. Astron. Astrophys., 19 (1981), 137–162. CrossRefGoogle Scholar
Salmon, J., Charnoz, S., Crida, A., Brahic, A.. Long-term and large-scale viscous evolution of dense planetary rings. Icarus, 209 (2010), 771–785. CrossRefGoogle Scholar
Salo, H.. Numerical simulations of dense collisional systems. Icarus, 90 (1991), 254–270. CrossRefGoogle Scholar
Salo, H.. Gravitational wakes in Saturn’s rings. Nature, 359 (1992), 619–621. CrossRefGoogle Scholar
Salo, H.. Simulations of dense planetary rings. III. Self-gravitating identical particles. Icarus, 117 (1995), 287–312. CrossRefGoogle Scholar
Salo, H., Schmidt, J., Spahn, F.. Viscous Overstability in Saturn’s B Ring. I. Direct Simulations and Measurement of Transport Coefficients. Icarus, 153 (2001), 295–315. CrossRefGoogle Scholar
Schmidt, J., Salo, H.. Weakly Nonlinear Model for Oscillatory Instability in Saturn’s Dense Rings. Physical Review Letters, 90 (2003), 6, 061102. CrossRefGoogle ScholarPubMed
Schmidt, J., Salo, H., Spahn, F., Petzschmann, O.. Viscous Overstability in Saturn’s B-Ring. II. Hydrodynamic Theory and Comparison to Simulations. Icarus, 153 (2001), 316–331. CrossRefGoogle Scholar
Schmit, U., Tscharnuter, W. M.. A fluid dynamical treatment of the common action of self-gravitation, collisions, and rotation in Saturn’s B-ring. Icarus, 115 (1995), 304–319. CrossRefGoogle Scholar
M. Seiß. Moonlets in Saturn’s dense rings. PhD thesis (2009).
Seiß, M., Spahn, F., Sremčević, M., Salo, H.. Structures induced by small moonlets in Saturn’s rings: Implications for the Cassini Mission. Geophysical Research Letters, 32 (2005), 11205. CrossRefGoogle Scholar
Showalter, M. R.. Visual detection of 1981S13, Saturn’s eighteenth satellite, and its role in the Encke gap. Nature, 351 (1991), 709–713. CrossRefGoogle Scholar
Showalter, M. R., Cuzzi, J. N., Marouf, E. A., Esposito, L. W.. Satellite ’wakes’ and the orbit of the Encke Gap moonlet. Icarus, 66 (1986), 297–323. CrossRefGoogle Scholar
Shu, F. H., Dones, L., Lissauer, J. J., Yuan, C., Cuzzi, J. N.. Nonlinear spiral density waves - Viscous damping. Astrophysical Journal, 299 (1985), 542–573. CrossRefGoogle Scholar
Shukhman, I. G.. Collisional Dynamics of Particles in Saturn’s Rings. Sov. Astron., 28 (1984), 574. Google Scholar
Spahn, F.. Scattering properties of a moonlet (satellite) embedded in a particle ring - Application to the rings of Saturn. Icarus, 71 (1987), 69–77. CrossRefGoogle Scholar
Spahn, F., Albers, N., Sremcevic, M., Thornton, C.. Kinetic description of coagulation and fragmentation in dilute granular particle ensembles. Europhysics Letters, 67 (2004), 545–551. CrossRefGoogle Scholar
Spahn, F., Schmidt, J., Petzschmann, O., Salo, H.. Note: Stability analysis of a Keplerian disk of granular grains: Influence of thermal diffusion. Icarus, 145 (2000), 657–660. CrossRefGoogle Scholar
Spahn, F., Scholl, H., Hertzsch, J.. Structures in planetary rings caused by embedded moonlets. Icarus, 111 (1994), 514–535. CrossRefGoogle Scholar
Spahn, F., Sponholz, H.. Existence of moonlets in Saturn’s rings inferred from the optical depth profile. Nature, 339 (1989), 607–608. CrossRefGoogle Scholar
Spahn, F., Sremčević, M.. Density patterns induced by small moonlets in Saturn’s rings? Astronomy and Astrophysics, 358 (2000), 368–372. Google Scholar
Spahn, F., Wiebicke, H.-J.. Long-term gravitational influence of moonlets in planetary rings. Icarus, 77 (1989), 124–134. CrossRefGoogle Scholar
Sremcevic, M., Stewart, G. R., Albers, N., Colwell, J. E., Esposito, L. W.. Density Waves in Saturn’s Rings: Non-linear Dispersion and Moon Libration Effects. Bulletin of the American Astronomical Society, 40 (2008), 430. Google Scholar
Sremčević, M., Schmidt, J., Salo, H., Seiß, M., Spahn, F., Albers, N.. A belt of moonlets in Saturn’s A ring. Nature, 449 (2007), 1019–1021. CrossRefGoogle ScholarPubMed
Sremčević, M., Spahn, F., Duschl, W. J.. Density structures in perturbed thin cold discs. Monthly Notices Royal Astron. Soc., 337 (2002), 1139–1152. CrossRefGoogle Scholar
G. R. Stewart, D. N. C. Lin, P. Bodenheimer. Collision-induced transport processes in planetary rings. Planetary Rings (R. Greenberg & A. Brahic, editor) (1984), 447–512.
Thomson, F. S., Marouf, E. A., Tyler, G. L., French, R. G., Rappoport, N. J.. Periodic microstructure in Saturn’s rings A and B. Geophysical Research Letters, 34 (2007), 24203. CrossRefGoogle Scholar
Tiscareno, M. S., Burns, J. A., Hedman, M. M., Porco, C. C., The Population of Propellers in Saturn’s A Ring. Astronomical Journal, 135 (2008), 1083–1091. CrossRefGoogle Scholar
Tiscareno, M. S., Burns, J. A., Hedman, M. M., Porco, C. C., Weiss, J. W., Dones, L., Richardson, D. C., Murray, C. D., 100-metre-diameter moonlets in Saturn’s A ring from observations of ’propeller’ structures. Nature, 440 (2006), 648–650. CrossRefGoogle ScholarPubMed
Tiscareno, M. S., Burns, J. A., Nicholson, P. D., Hedman, M. M., Porco, C. C.. Cassini imaging of Saturn’s rings. II. A wavelet technique for analysis of density waves and other radial structure in the rings. Icarus, 189 (2007), 14–34. CrossRefGoogle Scholar
Tiscareno, M. S., Burns, J. A., Sremčević, M., Beurle, K., Hedman, M. M., Cooper, N. J., Milano, A. J., Evans, M. W., Porco, C. C., Spitale, J. N., Weiss, J. W.. Physical Characteristics and Non-Keplerian Orbital Motion of ”Propeller” Moons Embedded in Saturn’s Rings. Astrophysical Journal Letters, 718 (2010), L92–L96. CrossRefGoogle Scholar
Ward, W. R.. On the radial structure of Saturn’s rings. Geophysical Research Letters, 8 (1981), 641–643. CrossRefGoogle Scholar
S. J. Weidenschilling, C. R. Chapman, D. R. Davis, R. Greenberg. Ring particles - Collisional interactions and physical nature. Planetary Rings (1984) pages 367–415.
Wisdom, J., Tremaine, S.. Local simulations of planetary rings. Astronomical Journal, 95 (1988), 925–940. CrossRefGoogle Scholar
Zebker, H. A., Marouf, E. A., Tyler, G. L.. Saturn’s rings - Particle size distributions for thin layer model. Icarus, 64 (1985), 531–548. CrossRefGoogle Scholar