Nonlinear dynamics of inclined films under low-frequency forcing

Abstract

The evolution of an inclined liquid film, subjected to regular inlet disturbances of small frequency, f, is studied experimentally and computationally. The fluorescence imaging method is used to quantitatively document film thickness at a downstream window of the flow channel, and a Galerkin finite-element solution of the Navier-Stokes equation of motion is invoked to predict the entire spatio-temporal dynamics of the free surface. Experiments confirm that, below a certain frequency, f(p), the regular wave train is destroyed by the appearance of one or more parasitic crests behind each major wave. Experiments and simulations indicate that parasitic crests are not the result of spatially unlocalized instabilities in the substrate, but originate in a regular way from a depression developing at the tails of growing solitary waves. Their downstream fate is dictated by the proximity of the next major wave, and thus different scenarios are predicted and observed for fapproximate tof(p) and f<f(p). A theoretical explanation of the phenomenon is suggested in terms of the radiation properties of growing solitary crests, as described by Chang, Demekhin, and Kalaidin [SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 58, 1246 (1998)]. (C) 2004 American Institute of Physics.