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

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...