Article: Lawney BP, Jenkins JT and Burns JA (2012). “Collisional features in a model of a planetary ring.” Icarus 220(2): 383-391.
Abstract: Images taken by the Cassini spacecraft display numerous “propellers”, telltale disturbances detected in Saturn’s outer A ring. In conventionally accepted models (Seiss, M., Spahn, F., Sremcevic, M., Salo, H. [2005]. Geophys. Res. Lett. 32, L11205; Lewis, M., Stewart, G. [2009]. Icarus 199, 387-412), unseen moonlets are considered to generate these structures by gravitationally stirring the shearing Kepler flow of ring particles. The morphology and scale of these structures likely depend on both gravity and collisions. However, with a goal to understand one aspect of the development of real propellers, and motivated by similar features observed in terrestrial granular systems, we here study only the collisional effects on propeller-like feature formation, entirely omitting the gravitational attraction between the moonlet and the particles.
Our investigation employs a combination of simulation and continuum analysis to examine the extent to which dissipative collisions between ring particles and with a large obstacle might cause such features to form. Our simple, heuristic two-dimensional numerical simulations demonstrate that propeller-like features having many of the features seen in gravitating systems can form. Our continuum theory predicts that, at observed ring densities, the magnitudes of relative particle speeds and thermal speeds (i.e., kinetic granular temperatures) imply that the flow with respect to the moonlet is supersonic. As a consequence, these propeller-like features could be interpreted as the locus of a granular shock across which the flow experiences significant, almost discontinuous, changes in flow properties.
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