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B. Scheichl, R. I. Bowles:
"Short-to-Long-Scale Interaction in Weakly Viscous Super- to Transcritical Liquid-Layer Flows";
Talk: Applied Mathematics Seminars, Department of Mathematics, University College London, UK; 2016-11-22.

We consider a thin liquid film past a horizontal plate under the action of gravity acting vertically, surface tension, and relatively low viscosity. A manifold of intriguing phenomena arise given the three disparate length scales involved: distance from jet impingement driving the layer to the trailing edge of the plate (long), height of the film (short), and, under transcritical conditions, an intrinsic intermediate one at play immediately upstream of the trailing edge. 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 (unsteady) hydraulic jumps are identified.

boundary layers, capillary flows, free-surface flows, short-scale interaction, thin flims, transcritical flows, triple deck

http://publik.tuwien.ac.at/files/publik_254380.pdf