Nonlinear waves on the surface of a falling liquid film. Part 2. Bifurcations of the first-family waves and other types of nonlinear waves

Abstract

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 plane. A bifurcation analysis of the wave regimes found in Part 1 of this work (Tsvelodub & Trifonov 1991), and of the new wave families obtained here in Part 2, has been carried out. It is demonstrated that there is a great number of different steady-state travelling wave classes which are parameterized by wavenumber at a fixed Reynolds number for a given liquid. It is shown that some of them quantitatively agree with experimental results. The question of stability of various wave regimes with respect to two-dimensional infinitesimal disturbances is examined and it is shown that one particular wave family is found. The most amplified disturbances are evaluated.