On transcritical states in viscous flow passing the edge of a horizontal plate

This contribution puts forward some recent advances in the rigorous (asymptotic) theory of gravity- (and capillarity-)driven shallow flow of a viscous liquid past a horizontal plate, originating in jet impingement oblique to it. Hence, our concern is twofold: with steady developed flow over the distance from the jet centre to the trailing edge of the plate, referred to as a pronounced hydraulic jump blurred by viscous diffusion; with the predominantly inviscid transcritical limit arising near the edge due to scale reduction given an intrinsic expansive singularity taking place there. In the latter situation envisaged briefly, condensing nonlinear inertial effects, weak time dependence, and (very) weak streamline curvature as the essential ingredients into a distinguished limit demonstrates the generation of a weak (transcritical) hydraulic jump by a plate-mounted obstacle. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)