# Hydrodynamics of Saturn’s Dense Rings

Mathematical Modelling of Natural Phenomena (2011)

- Volume: 6, Issue: 4, page 191-218
- ISSN: 0973-5348

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topSeiß, M., and Spahn, F.. "Hydrodynamics of Saturn’s Dense Rings." Mathematical Modelling of Natural Phenomena 6.4 (2011): 191-218. <http://eudml.org/doc/222216>.

@article{Seiß2011,

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. },

author = {Seiß, M., Spahn, F.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {granular gas; instabilities; hydrodynamics; planetary rings},

language = {eng},

month = {7},

number = {4},

pages = {191-218},

publisher = {EDP Sciences},

title = {Hydrodynamics of Saturn’s Dense Rings},

url = {http://eudml.org/doc/222216},

volume = {6},

year = {2011},

}

TY - JOUR

AU - Seiß, M.

AU - Spahn, F.

TI - Hydrodynamics of Saturn’s Dense Rings

JO - Mathematical Modelling of Natural Phenomena

DA - 2011/7//

PB - EDP Sciences

VL - 6

IS - 4

SP - 191

EP - 218

AB - 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.

LA - eng

KW - granular gas; instabilities; hydrodynamics; planetary rings

UR - http://eudml.org/doc/222216

ER -

## References

top- N. Albers, F. Spahn. The influence of particle adhesion on the stability of agglomerates in Saturn’s rings. Icarus, 181 (2006), 292–301.
- J. P. Andrews. Theory of Collision of Spheres of Soft Metals. Phil.Mag.S.7, 9 (1930), 58, 593–610. Zbl56.1246.01
- S. Araki, S. Tremaine. The dynamics of dense particle disks. Icarus, 65 (1986), 83–109.
- J. M. Barbara, L. W. Esposito. Moonlet Collisions and the Effects of Tidally Modified Accretion in Saturn’s F Ring. Icarus, 160 (2002), 1, 161–171.
- N. Borderies. Ring dynamics. Celestial Mechanics and Dynamical Astronomy, 46 (1989), 207–230. Zbl0682.70008
- N. Borderies, P. Goldreich, S. Tremaine. Sharp edges of planetary rings. Nature, 299 (1982), 209–211.
- N. Borderies, P. Goldreich, S. Tremaine. Unsolved problems in planetary ring dynamics. In Planetary Rings (1984) pages 713–734.
- N. Borderies, P. Goldreich, S. Tremaine. A granular flow model for dense planetary rings. Icarus, 63 (1985), 406–420.
- N. Borderies, P. Goldreich, S. Tremaine. Nonlinear density waves in planetary rings. Icarus, 68 (1986), 522–533.
- N. Borderies, P. Goldreich, S. Tremaine. The formation of sharp edges in planetary rings by nearby satellites. Icarus, 80 (1989), 344–360.
- J. J. Brey, J. W. Dufty, C. S. Kim, A. Santos. Hydrodynamics for granular flow at low density. Physical Review E, 58 (1998), 4638–4653.
- F. G. Bridges, A. Hatzes, D. N. C. Lin. Structure, stability and evolution of Saturn’s rings. Nature, 309 (1984), 333–335.
- N. Brilliantov, F. Spahn, J.-M. Hertzsch, T. Pöschel. Model for collisions in granular gases. Physical Review E, 53 (1996), 5382–5392.
- N. V. Brilliantov, N. Albers, F. Spahn, T Pöschel, Collision dynamics of granular particles with adhesion. Phys. Rev. E, 76 (2008), 051302.
- R. M. Canup, L. W. Esposito. Accretion in the Roche zone: Coexistence of rings and ring moons. Icarus, 113 (1995), 331–352.
- S. Charnoz, J. Salmon, A. Crida. The recent formation of Saturn’s moonlets from viscous spreading of the main rings. Nature, 465 (2010), 752–754.
- J. E. Colwell, J. H. Cooney, L. W. Esposito, M. Sremčević. Density waves in Cassini UVIS stellar occultations. 1. The Cassini Division. Icarus, 200 (2009), 574–580.
- J. E. Colwell, L. W. Esposito, M. Sremčević. Self-gravity wakes in Saturn’s A ring measured by stellar occultations from Cassini. Geophysical Research Letters, 33 (2006), 7201.
- J. E. Colwell, L. W. Esposito, M. Sremčević, G. R. Stewart, W. E. McClintock. Self-gravity wakes and radial structure of Saturn’s B ring. Icarus, 190 (2007), 127–144.
- 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.
- J. N. Cuzzi, J. D. Scargle. Wavy edges suggest moonlet in Encke’s gap. Astrophysical Journal, 292 (1985), 276–290.
- H. Daisaka, H. Tanaka, S. Ida. Viscosity in a Dense Planetary Ring with Self-Gravitating Particles. Icarus, 154 (2001), 296–312.
- D. R. Davis, S. J. Weidenschilling, C. R. Chapman, R. Greenberg. Saturn ring particles as dynamic ephemeral bodies. Science, 224 (1984), 744–747.
- S. F. Dermott, C. D. Murray. The dynamics of tadpole and horseshoe orbits. I - Theory. II - The coorbital satellites of Saturn. Icarus, 48 (1981), 1–22.
- S. F. Dermott, C. D. Murray, A. T. Sinclair. The narrow rings of Jupiter, Saturn and Uranus. Nature, 284 (1980), 309–313.
- L. W. Esposito, M. Ocallaghan, R. A. West. The structure of Saturn’s rings - Implications from the Voyager stellar occultation. Icarus, 56 (1983), 439–452.
- R. G. French, P. D. Nicholson. Saturn’s Rings II. Particle sizes inferred from stellar occultation data. Icarus, 145 (2000), 502–523.
- P. Goldreich, S. Tremaine. The excitation and evolution of density waves. Astrophysical Journal, 222 (1978), 850–858.
- P. Goldreich, S. D. Tremaine. The velocity dispersion in Saturn’s rings. Icarus, 34 (1978), 227–239.
- A. Hatzes, F. G. Bridges, D. N. C. Lin. Collisional properties of ice spheres at low impact velocities. Mon. Not. R. Astr. Soc., 231 (1988), 1091–1115.
- M. M. Hedman, P. D. Nicholson, H. Salo, B. D. Wallis, B. J. Buratti, K. H. Baines, R. H. Brown, R. N. Clark. Self-Gravity Wake Structures in Saturn’s A Ring Revealed by Cassini VIMS. Astronomical Journal, 133 (2007), 2624–2629.
- D. Heißelmann, J. Blum, H. J. Fraser, K. Wolling. Microgravity experiments on the collisional behavior of saturnian ring particles. Icarus, 206 (2010), 424–430.
- M. Henon. A simple model of Saturn’s rings. Nature, 293 (1981), 33–35.
- J.-M. Hertzsch, H. Scholl, F. Spahn, I. Katzorke. Simulation of collisions in planetary rings. Astronomy and Astrophysics, 320 (1997), 319–324.
- J. Jenkins, M. Richman. Grad’s 13-moment system for a dense gas of inelastic spheres. Arch. Ration. Mech. Anal., 87 (1985), 355–377. Zbl0617.76085
- H. N. Latter, G. I. Ogilvie. The linear stability of dilute particulate rings. Icarus, 184 (2006), 498–516.
- H. N. Latter, G. I. Ogilvie. Dense planetary rings and the viscous overstability. Icarus, 195 (2008), 725–751.
- H. N. Latter, G. I. Ogilvie. The viscous overstability, nonlinear wavetrains, and finescale structure in dense planetary rings. Icarus, 202 (2009), 565–583.
- H. N. Latter, G. I. Ogilvie. Hydrodynamical simulations of viscous overstability in Saturn’s rings. Icarus, 210 (2010), 318–329.
- M. C. Lewis, G. R. Stewart. Collisional Dynamics of Perturbed Planetary Rings. I. Astronomical Journal, 120 (2000), 3295–3310.
- D. N. C. Lin, P. Bodenheimer. On the stability of Saturn’s rings. Astrophysical Journal, 248 (1981), L83–L86.
- D. N. C. Lin, J. E. Pringle. A viscosity prescription for a self-gravitating accretion disc. Monthly Notices Royal Astron. Soc., 225 (1987), 607–613.
- J. J. Lissauer, F. H. Shu, J. N. Cuzzi. Moonlets in Saturn’s rings. Nature, 292 (1981), 707–711.
- P.-Y. Longaretti. Saturn’s main ring particle size distribution - an analytic approach. Icarus, 81 (1989), 51–73.
- D. Lynden-Bell, J. Pringle. The evolution of viscous discs and the origin of the nebular variables. Mon.Not.Roy.Astron.Soc, 168 (1974), 603–637.
- J.-M. Petit, M. Henon. A numerical simulation of planetary rings. III - Mass segregation, ring confinement, and gap formation. Astronomy and Astrophysics, 199 (1988), 343–356. Zbl0666.70014
- C. C. Porco. S/2005 S 1. IAU Circ., 8524 (2005), 1.
- J. E. Pringle. Accretion discs in astrophysics. Ann. Rev. Astron. Astrophys., 19 (1981), 137–162.
- J. Salmon, S. Charnoz, A. Crida, A. Brahic. Long-term and large-scale viscous evolution of dense planetary rings. Icarus, 209 (2010), 771–785.
- H. Salo. Numerical simulations of dense collisional systems. Icarus, 90 (1991), 254–270.
- H. Salo. Gravitational wakes in Saturn’s rings. Nature, 359 (1992), 619–621.
- H. Salo. Simulations of dense planetary rings. III. Self-gravitating identical particles. Icarus, 117 (1995), 287–312.
- H. Salo, J. Schmidt, F. Spahn. Viscous Overstability in Saturn’s B Ring. I. Direct Simulations and Measurement of Transport Coefficients. Icarus, 153 (2001), 295–315.
- J. Schmidt, H. Salo. Weakly Nonlinear Model for Oscillatory Instability in Saturn’s Dense Rings. Physical Review Letters, 90 (2003), 6, 061102.
- J. Schmidt, H. Salo, F. Spahn, O. Petzschmann. Viscous Overstability in Saturn’s B-Ring. II. Hydrodynamic Theory and Comparison to Simulations. Icarus, 153 (2001), 316–331.
- U. Schmit, W. M. Tscharnuter. A fluid dynamical treatment of the common action of self-gravitation, collisions, and rotation in Saturn’s B-ring. Icarus, 115 (1995), 304–319.
- M. Seiß. Moonlets in Saturn’s dense rings. PhD thesis (2009).
- M. Seiß, F. Spahn, M. Sremčević, H. Salo. Structures induced by small moonlets in Saturn’s rings: Implications for the Cassini Mission. Geophysical Research Letters, 32 (2005), 11205.
- M. R. Showalter. Visual detection of 1981S13, Saturn’s eighteenth satellite, and its role in the Encke gap. Nature, 351 (1991), 709–713.
- M. R. Showalter, J. N. Cuzzi, E. A. Marouf, L. W. Esposito. Satellite ’wakes’ and the orbit of the Encke Gap moonlet. Icarus, 66 (1986), 297–323.
- F. H. Shu, L. Dones, J. J. Lissauer, C. Yuan, J. N. Cuzzi. Nonlinear spiral density waves - Viscous damping. Astrophysical Journal, 299 (1985), 542–573.
- I. G. Shukhman. Collisional Dynamics of Particles in Saturn’s Rings. Sov. Astron., 28 (1984), 574. Zbl0598.70007
- F. Spahn. Scattering properties of a moonlet (satellite) embedded in a particle ring - Application to the rings of Saturn. Icarus, 71 (1987), 69–77.
- F. Spahn, N. Albers, M. Sremcevic, C. Thornton. Kinetic description of coagulation and fragmentation in dilute granular particle ensembles. Europhysics Letters, 67 (2004), 545–551.
- F. Spahn, J. Schmidt, O. Petzschmann, H. Salo. Note: Stability analysis of a Keplerian disk of granular grains: Influence of thermal diffusion. Icarus, 145 (2000), 657–660.
- F. Spahn, H. Scholl, J. Hertzsch. Structures in planetary rings caused by embedded moonlets. Icarus, 111 (1994), 514–535.
- F. Spahn, H. Sponholz. Existence of moonlets in Saturn’s rings inferred from the optical depth profile. Nature, 339 (1989), 607–608.
- F. Spahn, M. Sremčević. Density patterns induced by small moonlets in Saturn’s rings?Astronomy and Astrophysics, 358 (2000), 368–372.
- F. Spahn, H.-J. Wiebicke. Long-term gravitational influence of moonlets in planetary rings. Icarus, 77 (1989), 124–134.
- M. Sremcevic, G. R. Stewart, N. Albers, J. E. Colwell, L. W. Esposito. Density Waves in Saturn’s Rings: Non-linear Dispersion and Moon Libration Effects. Bulletin of the American Astronomical Society, 40 (2008), 430.
- M. Sremčević, J. Schmidt, H. Salo, M. Seiß, F. Spahn, N. Albers. A belt of moonlets in Saturn’s A ring. Nature, 449 (2007), 1019–1021.
- M. Sremčević, F. Spahn, W. J. Duschl. Density structures in perturbed thin cold discs. Monthly Notices Royal Astron. Soc., 337 (2002), 1139–1152.
- 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.
- F. S. Thomson, E. A. Marouf, G. L. Tyler, R. G. French, N. J. Rappoport. Periodic microstructure in Saturn’s rings A and B. Geophysical Research Letters, 34 (2007), 24203.
- M. S. Tiscareno, J. A. Burns, M. M. Hedman, C. C. Porco, The Population of Propellers in Saturn’s A Ring. Astronomical Journal, 135 (2008), 1083–1091.
- M. S. Tiscareno, J. A. Burns, M. M. Hedman, C. C. Porco, J. W. Weiss, L. Dones, D. C. Richardson, C. D. Murray, 100-metre-diameter moonlets in Saturn’s A ring from observations of ’propeller’ structures. Nature, 440 (2006), 648–650.
- M. S. Tiscareno, J. A. Burns, P. D. Nicholson, M. M. Hedman, C. C. Porco. 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.
- M. S. Tiscareno, J. A. Burns, M. Sremčević, K. Beurle, M. M. Hedman, N. J. Cooper, A. J. Milano, M. W. Evans, C. C. Porco, J. N. Spitale, J. W. Weiss. Physical Characteristics and Non-Keplerian Orbital Motion of ”Propeller” Moons Embedded in Saturn’s Rings. Astrophysical Journal Letters, 718 (2010), L92–L96.
- W. R. Ward. On the radial structure of Saturn’s rings. Geophysical Research Letters, 8 (1981), 641–643.
- S. J. Weidenschilling, C. R. Chapman, D. R. Davis, R. Greenberg. Ring particles - Collisional interactions and physical nature. Planetary Rings (1984) pages 367–415.
- J. Wisdom, S. Tremaine. Local simulations of planetary rings. Astronomical Journal, 95 (1988), 925–940.
- H. A. Zebker, E. A. Marouf, G. L. Tyler. Saturn’s rings - Particle size distributions for thin layer model. Icarus, 64 (1985), 531–548.

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