Other
Scientific paper
Oct 2000
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000dps....32.4909s&link_type=abstract
American Astronomical Society, DPS Meeting #32, #49.09; Bulletin of the American Astronomical Society, Vol. 32, p.1089
Other
Scientific paper
Local simulations with up to 60 \ 000 selfgravitating dissipatively colliding particles indicate that dense rings with τ > 1 can be overstable, with parameter values appropriate for Saturn's B ring. These axisymmetric oscillations, with scale ~ 100 meters generally coexist with inclined Julian-Toomre type wakes. Similar oscillatory behavior is also obtained in an approximation where the particle-particle gravity is replaced by an enhanced frequency of vertical oscillations, Ω z/Ω >1. These systems can be more easily studied analytically, as in the absence of wakes they possess a spatially uniform ground state. To facilitate quantitative hydrodynamical studies of overstability we have measured the transport coefficients (shear viscosity ν , bulk viscosity ζ and kinetic heat conductivity κ ) for systems with Ω z/Ω =3.6, \ 2.0, \ 1.0. Both local and nonlocal contributions to momentum and energy flux are taken into account, the latter being dominant in dense systems with large impact frequency. In this limit we find ζ /ν ≈ 2, κ /ν ≈ 4. The dependency of pressure, viscosity and dissipation on density and kinetic temperature changes is also estimated. Simulations indicate that the condition for overstability is β > β cr ~ 1, where β =dlog(ν )/dlog(τ ). This condition is more stringent than the β cr ~ 0 suggested by the linear stability analysis in Schmit and Tscharnuter (1995, Icarus 115: 304), where the system was assumed to stay isothermal even when perturbed. However, it agrees with the non-isothermal analysis in Spahn et al. (2000, Icarus 145: 657). The increased stability is partially due to the inclusion of temperature oscillations in the analysis, and partially to bulk viscosity exceeding shear viscosity. A detailed comparison between simulations and hydrodynamical analysis is given in an accompanying presentation by Schmidt et al.
Salo Heikki
Schmidt Jonas
Spahn Frank
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