Supercritical flow overpassing forward- or backward-facing steps non-orthogonal to the flow direction

The work proposes and discusses a theoretical approach to predict the behavior of an open-channel supercritical flow that overpasses a step, either forward or backward facing, non-orthogonal to the flow direction. In this case, a sequence of oblique shock waves and expansion fans is generated close to and downstream of the step. The proposed model is verified by comparing the theoretical predictions with the results provided by a two-dimensional, depth averaged numerical model. Applications include the combined use of oblique steps and abrupt wall deflections to suppress wave fronts that characterize supercritical flow in channel bends. Special attention is devoted to the supercritical to subcritical transition (and vice versa) in overpassing a forward-facing step; this is found to be a rather intriguing problem characterized by complex solutions and by hysteresis. Besides the classic smooth (everywhere supercritical) and choked (with a hydraulic jump and a subcritical flow upstream of the step) solutions, an additional intermediated flow configuration can occur for particular characteristics of the supercritical current and step height. The domain of existence of the different solutions, as well as the hysteresis domain, are obtained based on the theoretical and the numerical models.