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H. Salo (Div. of Astronomy, Univ. of Oulu), J. Schmidt, F. Spahn (Dept. of Nonlinear Dynamics, Univ. of Potsdam)
Local simulations with up to 60 \ 000 selfgravitating dissipatively colliding particles indicate that dense rings with \tau > 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, \Omegaz/\Omega >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 \nu, bulk viscosity \zeta and kinetic heat conductivity \kappa) for systems with \Omegaz/\Omega=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 \zeta/\nu \approx 2, \kappa/\nu \approx 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 \beta > \betacr ~1, where \beta=dlog(\nu)/dlog(\tau). This condition is more stringent than the \betacr ~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.
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