Viscous overstability (oscillatory instability) may play an important role in the formation of small scale structure in dense planetary rings such as Saturn’s $B$ ring. We investigate the growth and saturation of such modes in local particle simulations. Starting from a hydrodynamic model, we develop a set of ordinary differential equations to model the evolution of the amplitudes of the linearly overstable modes in the nonlinear regime. The NASA/ESA space probe Cassini can make direct observations of these modes in Saturn’s rings, including their sizes and temporal development.

• Received 25 October 2002

DOI:https://doi.org/10.1103/PhysRevLett.90.061102