A FULL-SCALE NUMERICAL STUDY OF INTERFACIAL INSTABILITIES IN THIN-FILM FLOWS

Surface wave instabilities in a two-dimensional thin draining film are studied by a direct numerical simulation of the full nonlinear system . A finite element method is used with an arbitrary Lagrangian-Euleria n formulation to handle the moving boundary problem. Both temporal and spatial stability analysis of the finite-amplitude nonlinear wave reg imes are done. As the wavenumber is decreased below the linear cut-off wavenumber, supercritical sinusoidal waves occur as reported earlier from weakly nonlinear analysis and experiments. Further reduction in w avenumber makes the Fourier spectrum broad-banded resulting in solitar y humps. This transition from nearly sinusoidal permanent waveforms to solitary humps is found to go through a quasi-periodic regime. The ph ase boundaries for this quasi-periodic regime have been determined thr ough extensive numerical parametric search. Complex wave interaction p rocesses such as wave merging and wave splitting are discussed. In the exhaustive numerical simulations performed in this paper, no wave-bre aking tendency was observed, and it is speculated that the complex wav e-interaction processes such as wave merging and wave splitting curb t he tendency of the film to break.