On Steady Two-dimensional Free-surface Flows with Spatially-varied Discharges

In an open-channel, the transition of a flow from a subcritical to a supercritical state may occur as a result of a lateral inflow or outflow that produces a streamwise discharge variation. Apparently, such a transition cannot be modeled accurately by a conventional hydrostatic pressure approach. In this study, a depth-averaged model that accounts for the effects of a spatially-varied discharge and a non-hydrostatic pressure distribution was developed and applied to simulate the transcritical flow in a lateral-spillway channel and the subcritical flow in a main channel fitted with side weirs. The model results for the axial free-surface profile and variation of discharge in the main channel were compared with the results of a shallow-flow model and experimental data, thereby resulting in a closer match to the measurements than the shallow-flow model. Overall, the investigation results confirmed the efficiency and validity of the non-hydrostatic depth-averaged model in simulating the mean flow characteristics of the subcritical and transcritical free-surface flows with spatially increasing or decreasing discharges, thus demonstrating its potential to be used as a numerical tool in engineering practice.