Solitary waves on inclined films: Flow structure and binary interactions

Abstract

The downstream evolution of disturbances, introduced at the inlet of a liquid film flowing along an inclined plane wall, is studied numerically by solving the full, time-dependent Navier–Stokes equation. Computational results are validated against the predictions of spatial linear stability analysis and against detailed data of the entire evolution process. The structure of the flow field below the waves is analyzed, and the results are used to test assumptions frequently invoked in the theoretical study of film flow by long-wave equations. An interesting prediction is that solitary waves exhibit strongly nonparabolic velocity profiles in front of the main hump, including a slim region of backflow. The computational scheme is subsequently used to study solitary wave interactions. It is predicted that coalescence (the inelastic collision of two humps) is not inevitable but occurs only when the waves differ appreciably in height. Waves of similar size repel monotonically, whereas for intermediate differences in height a strong oscillatory interaction between the two humps is predicted. Encouraging qualitative agreement with the limited experimental information available is noted.