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A Granular Flow Model for Dense Planetary Rings

Borderies, Nicole and Goldreich, Peter and Tremaine, Scott (1985) A Granular Flow Model for Dense Planetary Rings. Icarus, 63 (3). pp. 406-420. ISSN 0019-1035.

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We study the viscosity of a differentially rotating particle disk in the limiting case where the particles are densely packed and their collective behavior resembles that of a liquid. The pressure tensor is derived from the equations of hydrodynamics and from a simple kinetic model of collisions described by Haff (1983). We find that density waves and narrow circular rings are unstable if the liquid approximation applies. The resulting development of nonlinear perturbations may give rise to “splashing” of the ring material in the vertical direction. These results may help in understanding the origin of the ellipticities of ringlets, the nonaxisymmetric features near the outer edge of the Saturnian B ring, and the unexplained residuals in kinematic models of the Saturnian and Uranian rings.

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Additional Information:© 1985 Academic Press Inc. Received February 4, 1985: revised March 18, 1985. N.B. acknowledges grants from ATP Planétologie 1983 and 1984. P.G. acknowledges support from NSF Grant AST-8313725 and NASA Grant NGL-05-002-003. S.T. acknowledges support from NSF Grants AST-8210463 and AST-8412365. We thank E. S. Phinney for pointing out the reference by Ziman (1979).
Funding AgencyGrant Number
ATP Planétologie 1983UNSPECIFIED
ATP Planétologie 1984UNSPECIFIED
Issue or Number:3
Record Number:CaltechAUTHORS:20130301-083144733
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Official Citation:Nicole Borderies, Peter Goldreich, Scott Tremaine, A granular flow model for dense planetary rings, Icarus, Volume 63, Issue 3, September 1985, Pages 406-420, ISSN 0019-1035, 10.1016/0019-1035(85)90054-5. (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:37221
Deposited By: Ruth Sustaita
Deposited On:01 Mar 2013 18:30
Last Modified:03 Oct 2019 04:45

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