Hydrodynamical Simulations of the Uranian Rings
Abstract
We investigate the global dynamics of the Uranian rings using a modified 2D smoothed particle hydrodynamic code combined with a 2D tree code used to compute the particletoparticle gravitational interactions. This code includes epicyclic fluid motion, nonaxisymmetric flow, local and nonlocal shear viscocity, selfconsistent scale height evolution, ringsatellites gravitational interaction and coevolution, and ring selfgravity. To follow the scale height of each particle we solve the vertical momentum equation for the flow using a RungeKutta scheme with a second order polynomial fit to the vertical behavior of the fluid pressure (Borderies, Goldreich, and Tremaine 1985. Icarus, 63, 406). The behavior of the fluid viscocity is obtained from Mosqueira (1996. Icarus, 122, 128) who found good agreement between an extension to the nonlocal viscocity model of Borderies, Goldreich, and Tremaine (1985) that includes local terms with the results of a local patchcode ring simulation. Our present viscocity model incorporates further terms which account for the epicyclic limit to the mean free path (Goldreich and Tremaine 1978. Icarus, 34, 227). This treatment covers both the high and low ring density regimes. Our approach treats the fluid work terms and internal energy selfconsistently even in the presence of a nonzero divergence of the fluid velocity. Even within a 2D framework the Uranian rings are so thin compared to their semimajor axes that radial resolution requires too many particles given our present computer resources. To address this issue we have developed a physical scaling that reduces the semimajor axis of the ring while preserving its width and, we believe, retains the relevant global satellitering dynamics. With a conservative value of the scaling parameter that reduces the ring's semimajor axis by a factor of 10, our scaling allows for savings between a factor of 20 in the case of synodic time scales, a factor of 200 for shear timescales, and a factor of 2000 for viscous timescales. In the present study we use this scaling to test the validity of the selfgravity model of eccentric ring precession (Goldreich and Tremaine 1979. Astron. J., 84, 1638).
 Publication:

AAS/Division for Planetary Sciences Meeting Abstracts #28
 Pub Date:
 September 1996
 Bibcode:
 1996DPS....28.1814M