Nominally two-dimensional waves in inclined film flow in channels of finite width

Abstract

Traveling waves in inclined film flow in channels of finite width are never truly two-dimensional (2D) because of a long-range effect of sidewalls. The present study documents the characteristics of the first waves that are observed beyond the primary instability (termed nominally 2D) by taking measurements in a 3000 mm long inclined facility with adjustable width up to 450 mm using a fluorescence imaging technique. It is observed that nominally 2D waves are very persistent structures with their crests attaining a parabolic shape, which is symmetric with respect to the channel centerplane irrespective of the 3D content of the inlet forcing. The apex curvature of the parabola varies inversely with channel width and Reynolds number. The wave height is maximum at the centerplane and decreases to zero at the sidewalls, irrespective of the wetting properties of the system. The linear phase velocity of nominally 2D waves is always lower than predicted by the theory for small amplitude, 2D waves, and significantly in narrow channels and/or small inclinations. The above characteristics are shown to explain discrepancies between theory and observations, in particular the recently reported deviation of the onset of the primary instability from the classical prediction [M. Vlachogiannis et al., Phys. Fluids 22, 012106 (2010)].