Turbulent viscosity and lifetime of Saturn's rings Academic Article uri icon


  • 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=CG2Σ2/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 ) are not likely much younger than the solar system.

publication date

  • January 1, 2006