IRREGULAR WAVES ON VISCOUS FALLING FILMS

A thin viscous film falling down a vertical plane is studied. In particular, the interfacial wave is analyzed via a long-wave evolution equation of Benney type. Three instabilities are discussed in relation to the generation of chaotic waves observed in many experiments. The primary wave motion is induced by the surface-wave instability, and the waves can subsequently become chaotic due to spatially-subharmonic and three-dimensional instabilities. These secondary instabilities are demonstrated by numerical simulation in a spatially periodic domain. The evolution equation contains a description of the deterministic chaos.