EVOLUTION OF ROLL WAVES RUNNING DOWN AN INCLINED PLANE

The method of fluid sheets is used to study the flow of a linear viscous fluid down an inclined plane, The linear stability of the steady Nusselt flow and the nonlinear evolution of large-amplitude waves are examined. The results from linear stability analysis agree very well with experimental data and other theoretical investigations. A finite-difference scheme is used to examine the evolution of nonlinear finite-amplitude waves. The dynamic nonlinear behavior seen experimentally is predicted, including phenomena not previously reported in other theoretical investigations, such as decreasing wave heights, wave breaking and the breakdown of an initially solitary disturbance into a series of waves. The computed wave forms include large-amplitude waves and capillary ripples running in front of them.