The evolution and subsequent dynamics of waves on a vertically falling liquid film

Abstract

The spatiotemporal evolution of periodic waves on a vertically falling water film was investigated at the Reynolds number Re=15–75 via physical and numerical experiments. Small periodic waves excited at a low frequency grow directly into teardrop-shaped tall pulses, small waves of an intermediate frequency first grow into close-packed humps and then into pulses sandwiching single capillary ripples, and small waves of a high frequency grow into nearly sinusoidal waves. The initial wave evolution causes the waves to accelerate at low frequencies or to decelerate at intermediate and high frequencies. The maximum deceleration occurs with the growth into the close-packed humps which then undergo the transition to the pulses without a change of the wave frequency, associated with rapid acceleration. Subsequently, the quasisteady, nearly sinusoidal waves of small amplitudes and short-separation pulses further develop into nearly solitary tall pulses through transitions of wave coalescence, associated with growth of transverse wavefront variation. The nearly sinusoidal waves of large amplitudes rapidly increase the transverse variations of wavefronts and then fade away. These spatiotemporal evolution scenarios are consistent with the predictions from the stability analysis of steady-state traveling waves and the numerical simulations of the temporal evolution of periodic waves reported in the literature. A comparison with the evolution of noise-driven natural waves suggests that the natural waves greatly compress the scenario of waves at an intermediate frequency and rapidly grow into nearly solitary pulses following the scenario. Furthermore, it was revealed that these evolution scenarios resemble the ones observed on falling films inclined slightly from the horizontal.