Solitary-like Wave Dynamics in Thin Liquid Films over a Vibrated Inclined Plane

Abstract

Solitary-like surface waves that originate from the spatio-temporal evolution of falling liquid films have been the subject of theoretical and experimental research due to their unique properties that are not readily observed in other physical systems. Here we investigate, experimentally and theoretically, the dynamics of solitary-like surface waves in a liquid layer on an inclined plane that is subjected to a harmonic low-frequency vibration in a range from 30 to 50 Hz. We employ a standard boundary layer model, which describes large-amplitude deformations of the film surface, assuming that it has a self-similar parabolic longitudinal flow velocity profile, to confirm the experimental results and to explain the interplay between the short-wavelength Faraday instability and long-wavelength gravitational instability. In particular, we demonstrate that the vibration results in a decrease in the average and peak amplitude of the long solitary-like surface waves. However, the speed of these waves remains largely unaffected by the vibration, implying that they may propagate over large distances almost without changing their amplitude, thus rendering them suitable for a number of practical applications, where the immunity of pulses that carry information to external vibrations is required.