Weakly nonlinear model for oscillatory instability in Saturn's dense rings.

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.