Nonlinear evolution of perturbations in a thin fluid layer during wave formation

Abstract

A mathematical model is presented for the state of a free surface of a thin fluid layer (a fluid film) in heat-mass-exchange processes of condensation and evaporation. The wave motion of a fluid film is studied under inhomogeneous surface tension. Nonlinear development of perturbations belonging to a continuous band of wave numbers on the surface of a thin fluid layer is investigated within the framework of a non-linear parabolic equation. It is shown that wave packets with carrier wave lying near the harmonic of maximum increment become self-ordered; as a result, a monochromatic wave is generated on the surface of the fluid film. When a wave packet is generated in the neighborhood of the neutral stability curve, one can observe a phenomenon of directed energy transfer to the waves in the neighborhood of the harmonic of maximum increment.