B. Scheichl, R. I. Bowles:
"Capillary Effects and Short-Scale Interaction in a Weakly Viscous Supercritical Overfall";
Talk: 24th International Congress on Theoretical and Applied Mechanics (ICTAM 2016), Montréal, Canada; 2016-08-21 - 2016-08-26; in: "Contributions to the Foundations of Multidisciplinary Research in Mechanics", J. M. Floryan (ed.); IUTAM, Vol. 2 / Montréal (2017), ISBN: 978-0-660-05459-9; Paper ID TS.FM08-3.04 (pp. 1058-1059), 2 pages.
We consider a thin liquid film past a semi-infinite horizontal plate under the action of gravity acting vertically, surface tension, and relatively low viscosity. This scenario comprises a manifold of effects at play, given the two disparate length scales involved: distance from jet impingement generating the layer to the trailing edge of the plate, height of the film. The yet not fully understood behaviour of a developed viscous film near the edge and previous studies on hydraulic jumps in weakly viscous horizontal layers motivate the present investigation. In sharp contrast to these, here the flow remains supercritical, and isolated regimes of strong viscous--inviscid interaction are dictated by the short length scale rather than the common shallow-water approximation. Specifically, we show how viscosity produces standing waves upstream of localised interaction and how weak capillarity modifies drastically the potential-flow singularity close to the edge, which in turn affects crucially its viscous regularisation.
capillary flows, critical flows, fractional derivative, free-surfce flows, triple deck
http://publik.tuwien.ac.at/files/PubDat_250539.pdf