Interfacial waves on sheared, thin liquid films

Measurements of waves on thin liquid films sheared by a turbulent gas flow are made in a horizontal rectangular channel of high aspect ratio. The effect of flow conditions on both well-developed and evolving wave fields is examined for glycerin-water solutions in the range of 8-30 cP. Observed transitions in wave type are found to depend largely on gas shear, and its effect on various wave properties is examined. The evolution and interaction of waves at flow conditions close to and moderately removed from neutral stability are then examined; spectral analysis of the measured surface height time series is used to determine the frequency distribution, speeds and phase coherence of waves. Bicoherence spectra reveal that thin film waves transfer energy both upward and downward in frequency. Downward transfer results from quadratic difference interactions between the fundamental and higher frequency modes, the most dramatic example being formation of a subharmonic wave on the lower viscosity films (;A nonlinear wave equation, valid for liquid Reynolds numbers of O(1 to 100) is derived to describe and predict the properties of thin film waves. The equation reveals the presence of both kinematic and dynamic disturbances which may (i) act together; or (ii) singularly dominate the wave field. Parameter ranges for the dominant behavior are determined from linear stability analysis of the equation and its reduced forms. Amplitude equations are integrated to predict evolution of finite amplitude waves at conditions which match experimental measurements, and qualitative agreement is obtained with the data. The simulations suggest that the low frequency disturbance observed experimentally results from difference interactions among the dominant waves. Examination of the equation suggests that the ability to transfer energy downward in frequency is related to the complex coupling coefficients present in the amplitude equations.