TY - JOUR

T1 - Turbulent viscosity and lifetime of Saturn's rings

AU - Griv, Evgeny

AU - Gedalin, Michael

N1 - Funding Information:
We thank Jessica Malibo for motivating this analysis. The authors have benefited from stimulating conversations with David Eichler, Yury Lyubarsky, Raphael Steinitz, and Chi Yuan. The first referee drew our attention to Shu et al.'s paper. We thank both anonymous referees for their useful comments and suggestions to improve the manuscript. This work was supported in part by the Israel Science Foundation, the Israeli Ministry of Immigrant Absorption in the framework of the program “KAMEA,” and the Binational U.S.–Israel Science Foundation.

PY - 2006/8/1

Y1 - 2006/8/1

N2 - The viscosity (the angular momentum flux) in the disk of mutually gravitating particles of Saturn's rings is investigated. The hydrodynamic theory of the gravitational Jeans-type instability of small gravity perturbations (e.g., those produced by spontaneous disturbances) of the disk is developed. It is suggested that in such a system the hydrodynamic turbulence may arise as a result of the instability. The turbulence is related to stochastic motions of "fluid" elements. The objective of this paper is to show that in the Jeans-unstable Saturnian ring disk the turbulent viscosity may exceed the ordinary microscopic viscosity substantially. The main result of local N-body simulations of planetary rings by Daisaka et al. (2001. Viscosity in a dense planetary ring with self-gravitating particles. Icarus 154, 296-312) is explained: in the presence of the gravitationally unstable density waves, the effective turbulent viscosity νeff is given as νeff = CG2 Σ2 / Ω3, where G, Σ, and Ω are the gravitational constant, the surface mass density of a ring, and the angular velocity, respectively, and the nondimensional correction factor C ≈ 10. We argue that both Saturn's main rings and their irregular of the order of 100 m or even less fine-scale structure (being recurrently created and destroyed on the time scale of an order of Keplerian period ∼ 10 h) are not likely much younger than the solar system.

AB - The viscosity (the angular momentum flux) in the disk of mutually gravitating particles of Saturn's rings is investigated. The hydrodynamic theory of the gravitational Jeans-type instability of small gravity perturbations (e.g., those produced by spontaneous disturbances) of the disk is developed. It is suggested that in such a system the hydrodynamic turbulence may arise as a result of the instability. The turbulence is related to stochastic motions of "fluid" elements. The objective of this paper is to show that in the Jeans-unstable Saturnian ring disk the turbulent viscosity may exceed the ordinary microscopic viscosity substantially. The main result of local N-body simulations of planetary rings by Daisaka et al. (2001. Viscosity in a dense planetary ring with self-gravitating particles. Icarus 154, 296-312) is explained: in the presence of the gravitationally unstable density waves, the effective turbulent viscosity νeff is given as νeff = CG2 Σ2 / Ω3, where G, Σ, and Ω are the gravitational constant, the surface mass density of a ring, and the angular velocity, respectively, and the nondimensional correction factor C ≈ 10. We argue that both Saturn's main rings and their irregular of the order of 100 m or even less fine-scale structure (being recurrently created and destroyed on the time scale of an order of Keplerian period ∼ 10 h) are not likely much younger than the solar system.

KW - Planets

KW - Rings-planets and satellites

KW - Saturn-instabilities and waves

UR - http://www.scopus.com/inward/record.url?scp=33745925610&partnerID=8YFLogxK

U2 - 10.1016/j.pss.2006.04.013

DO - 10.1016/j.pss.2006.04.013

M3 - Article

AN - SCOPUS:33745925610

VL - 54

SP - 794

EP - 807

JO - Planetary and Space Science

JF - Planetary and Space Science

SN - 0032-0633

IS - 8

ER -