Observations of solitary wave dynamics of film flows

Abstract

Experimental results are reported on non-stationary evolution and interactions of waves forming on water and water–glycerol solution flowing along an inclined plane. A nonlinear wave generation process leads to a large number of solitary humps with a wide variety of sizes. A uorescence imaging method is applied to capture the evolution of film height in space and time with accuracy of a few microns. Coalescence – the inelastic interaction of solitary waves resulting in a single hump – is found to proceed at a timescale correlated to the difference in height between the interacting waves. The correlation indicates that waves of similar height do not merge. Transient phenomena accompanying coalescence are reported. The front-running ripples recede during coalescence, only to reappear when the new hump recovers its teardrop shape. The tail of the resulting solitary wave develops an elevated substrate relative to the front, which decays exponentially in time; both observations about the tail confirm theoretical predictions. In experiments with water, the elevated back substrate is unstable, yielding to a tail oscillation with wavelength similar to that of the front-running ripples. This instability plays a key role in two complex interaction phenomena observed: the nucleation of a new crest between two interacting solitary humps and the splitting of a large hump (that has grown through multiple coalescence events) into solitary waves of similar size.