Capillary effects and short-scale interaction in a weakly viscous supercritical overfall

Abstract eng:
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 bores and hydraulic jumps in weakly viscous horizontal layers stimulate 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.

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