We consider a thin liquid film past a horizontal plate of finite length under the action of gravity acting vertically, potentially surface tension, and relatively low viscosity. A range of intriguing phenomena arise given the three disparate length scales involved: distance from layer by jet impingement driving the layer to the trailing edge of the plate (long), height of the film (short), and, undertranscritical conditions, an intrinsic intermediate one. The steady free overfall serves as a paradigm for triggering the destabilising effect of viscosity on the short scale upstream. In supercritical flow, this culminates in a self-sustained, localised wave crest, governed by viscous-inviscid interaction and set apart from the edge. In the transcritical limit, a generic transonic-flow singularity provokes an interactive Korteweg-de-Vries regime. Here several limits and the role of isolated surface protuberances are addressed, where so-called “marginal states” associated with weak hydraulic jumps are identified and predictions made for the position of such jumps.
(Joint work with Bernhard Scheichl TU Vienna)