**DPS Pasadena Meeting 2000, 23-27 October 2000**

*Session 49. Rings Posters*

Displayed, 1:00pm, Monday - 1:00pm, Friday, Highlighted Tuesday and Thursday, 3:30-6:30pm, C101-C105, C211
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## [49.09] Viscous overstability in Saturn's B-ring: selfgravitating simulations.\\

*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, \Omega_{z}/\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
\Omega_{z}/\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 > \beta_{cr}
~1, where \beta=dlog(\nu)/dlog(\tau). This condition
is more stringent than the \beta_{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.

The author(s) of this abstract have provided an email address
for comments about the abstract:
heikki.salo@oulu.fi

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