Nonlinear waves on the surface of a falling liquid film. Part 1. Waves of the first family and their stability

The paper is devoted to a theoretical analysis of nonlinear two-dimensional waves on the surface of a liquid film freely falling down a vertical plate. Using a model system of equations, steady-state travelling periodical wave regimes have been found numerically. It is shown that some of them agree quantitatively with experimental results. The question of the stability of various wave regimes with respect to two-dimensional infinitesimal disturbances is examined. The most-amplified disturbances are evaluated.