Three-dimensional wave dynamics on a failing film and associated mass transfer

The evolution of solitary waves into three-dimensional (30 waves was experimentally observed on a vertically falling water film at mainly Re = 10-100. At Re greater than 40, 2-D solitary waves are very unstable in the face of spanwise perturbations of approximately 2-cm wavelengths and disintegrate into isolated horseshoe-shaped solitary waves and clusters of dimples between the horseshoes, whereas wavefront modulations are limited to low levels at Re below 40. Horseshoes of larger velocities have larger curvature heads, and extend longer oblique legs upward. Curving capillary ripples preceding each horseshoe widen their wavelengths with an increase in the wavefront inclination, showing that the ripples possess the characteristics of the shallow-water capillary waves. The horseshoes may hold vortices inside, and they have similarities in shape and size to hairpin vortices observed in laminar-turbulent transition regions of boundary layers on walls. The disintegration of waves into dimples is caused by a capillary instability similar to the one for breakup of a cylindrical soap film. This transition of wave dynamics at Re approximate to 40 is associated with a drastic change in the mass transfer from the surface into the film.