Nappe Flow Surges down a Rough-Stepped Sloping Channel

Nappe flow applies to small discharges, and investigation of nappe flow surges helps to understand the mechanism of water flow in stepped open channels. The objective of this paper is to investigate the nappe flow surge propagation down stepped open channels. First, an analytical solution of dam-break shock waves or flood waves is derived. Then, the theoretical solution is used to calculate the wavefront and celerity and is verified using experiments on surging waters down a stepped slope in a 20-m-long and 0.5-m-wide open channel under three conditions: one for smooth bed surface and the others for rough bed surface glued with uniform sediment (of diameter $d_s=1.715\mathrm{mm}$ and $d_s=3.5\mathrm{mm}$). For calculating the wavefront propagation in a stepped open channel, a formula for resistance, composed of grain resistance and step geometry resistance, is developed. Unlike skimming flow, the roughness of step surface in the nappe flow regime influences the friction factor $f_s$. Results show that the friction factor increases with the relative roughness height ($d_s/d_0$). The theoretical solution for the wavefront location and celerity is then revised by combining the friction formula, and the revised solution is tested for a wide range of experimental data. Test results show that the revised solution fits the measured data quite well. Comparing with the solution previously derived, the revised solution derived in this study more accurately predicts the wavefront location and celerity for the nappe flow condition.