Steady solutions of inertial film flow along strongly undulated substrates

Steady flow of a liquid film along sinusoidal, steeply corrugated walls is investigated by finite-element simulation of the 2D Navier-Stokes equations. Resonance between the wall and capillary-gravity waves travelling against the flow defines a critical Re and separates the flow into a subcritical and a supercritical regime. Steep corrugations trigger extensive flow separation in both regimes. However, the separation characteristics-most notably the limiting behavior for very thin and very thick films-vary because of the different significance of capillary forces in the two regimes. For very steep corrugations, two intersecting solution branches co-exist. The present computational predictions are compared favorably with independent experimental observations.