How hydraulic jumps form downstream of a negative step with channel expansion: experimental and numerical investigations of the transitions between wave jumps and submerged jets

Weirs and sills, particularly negative steps, play a pivotal role in modulating water flow, inducing hydraulic jumps that efficiently dissipate downstream energy. Beyond their aesthetic appeal, these features hold crucial engineering significance. This study combines physical experiments and numerical simulations downstream of a negative step featuring an abrupt width expansion. The spontaneous alteration of water flow conditions upstream and downstream of the step results in distinct flow regimes. By considering the critical Froude number to sustain an undular jump without wave breaking on a flatbed, we establish a framework for evaluating energy loss. Our analysis successfully delineates the transition limit between wave jumps and submerged jets downstream of a negative step. The co-existence regime of both jumps is explained by the analysis showing that the additional energy loss induced by the negative step is larger for the wave jump compared to the submerged jet. The abrupt width expansion at the negative step significantly reduces the transition depth between the submerged jet and wave jump, attributed to energy loss with intricate three-dimensional vortex motions-exceeding losses incurred by the negative step alone. We delve into the detailed mechanisms of these transitions through a three-dimensional numerical simulation of the energy-loss process and water surface profiles downstream of the step with expansion. The maximum energy loss by the undular jump and the minimum energy loss by the submerged jet are defined by the wave steepness at the limit of maintaining the undular jump and the jet plunging angle capable of sustaining the submerged jet, respectively. Transitions between submerged jet and wave jump in negative steps determined by plunging jet angle and wave height.Submerged jets produce turbulent kinetic energy more rapidly than wave jumps due to the large eddies near the plunging jet point.In a step with an abrupt width expansion, the vertical vortex generated results in a larger energy dissipation.