Flow of a shallow film over a moving surface

Abstract

The von-Karman–Pohlhausen averaging technique is employed to build a reduced model for the flow of a shallow film from a sluice gate or impacting jet over a moving surface. The viscous drag exerted on the film by the moving wall acts to arrest flow counter to the direction of the wall's motion, and force an adjustment toward the wall speed. For a (normally) impacting jet, this results in a range of wall speeds for which a steady state is reached in which all the fluid is eventually recirculated to flow along the wall, with a distinctive “heel” forming upstream of the impact region. For wall speeds below this range, the flow counter to the wall cannot be arrested, and unsteady states result. For wall speeds above this range, a different steady state emerges in which fluid is immediately diverted through and downstream of the impact region, eliminating any heel. The steady, heeled flow states predicted by the reduced model are in qualitative agreement with numerical simulations of the full two-dimensional problem.