Inception Line of Air Entrainment for Converging Stepped Spillways

In the traditional stepped spillways with uniform width, the inception points of air entrainment along the spillway transverse direction generally remain at a similar distance from the spillway entrance, and can therefore be treated as a 2D problem. In the converging stepped spillways, the converging sidewall causes a nonuniform flow distribution along the spillway transverse direction, and a disturbed flow region is generated near the converging sidewall with significantly higher flow depth and discharge and lower air concentration. Their inception points are no longer a 2D problem and were investigated by physical experiments in this study. It was found that the line of the inception points curves downstream in the disturbed flow region and ended at the standing wave with limited air entrainment, while it formed the approximately straight line in the undisturbed flow region away from the converging sidewall. Therefore, the inception line of air entrainment in the converging stepped spillways can be described by the straight and curved lines and two intersections. The effects of the inlet flow discharge and the sidewall convergence angle were tested and analyzed. The expressions for the straight and curved lines and the two intersections are established, which can help to identify the inception line of air entrainment for the converging stepped spillways and make reasonable predictions.