A new model describing the dynamics of large-amplitude waves on laminar falling wavy films at high Reynolds numbers (Re>300) is presented. The model is based on second-order boundary layer theory and includes the pressure variation across the film as well as high-order viscous terms. The consistency and accuracy of the model is verified by comparing the linear stability results with Kapitza's classical boundary layer model and Orr- Sommerfeld studies of the two-dimensional Navier-Stokes equations. Numerical integration of a traveling wave simplification of the model predicts the existence of chaotic large-amplitude, nonperiodic waves, as observed in the experiments. The computed wave statistics such as wave celerities, root-mean-square (RMS) values of film thickness, probability density function (PDF), and film thickness power spectrum using the present model are in reasonable agreement with those measured on naturally excited fully developed flows at Re>300. The present model also overcomes the main deficiency of the classical boundary layer model (namely, negative wall shear stress) predicts large-amplitude waves (with peak to substrate ratios of 3 to 4) and gives better agreement with data.
Yu, L.Q., Wasden, F.K., Dukler, A.E., Balakotaiah, V., Nonlinear Evolution of Waves on Falling Films at High Reynolds Numbers, Phys. Fluids, American Institute of Physics, College Park, MD, Vol. 7(8), pp. 1886-1902, August, 1995.