Unsteady-State Hydraulic Characteristics of Overland Flow

Indoor experiments consisting of 15 flow discharges, six kinds of roughness, and five different gradients were systematically investigated to discover the evolution laws of rolling waves, flow regimes, and resistance characteristics. The results showed increasingly apparent production of rolling waves due to instability of overland flow on the slope surface when unit discharge increased. However, as discharge increased continuously, rolling waves disappeared. Meanwhile, the defined unit charge regions of rolling-wave flow decreased with increasing roughness. When slope gradient $J<0.1564$, the flow state index ($m$) of overland flow first increased and then decreased with increasing roughness. However, it decreased steadily when $J>0.1564$. Moreover, when $k_s\le 0.08\mathrm{mm}$, $m$ increased as the slope increased and decreased when $k_s\ge 0.08\mathrm{mm}$, with a mean value of 0.543. Thus, the overland flow on a slope is a mixed-flow zone dominated by transitional flow and supplemented by laminar flow. This is consistent with results obtained using the traditional discriminant method. However, the flow regimes existed in the laminar instability zone when a better discriminant method was adopted based on the viscosity-depth ratio. As for flow patterns, when the Froude number discriminant method was adopted, the water flow was supercritical flow. The resistance coefficient was inversely proportional to Reynolds number and was based on frictional resistance, thickness of the viscous sublayer, pressure drag, and roll waves resulting from the increasing-resistance phenomenon of roughness. Finally, a formula for calculating resistance is proposed based on the resistance characteristics [$f=(24/\mathrm{Re})+(\mathrm{14,041}/{\mathrm{Re}}_d^{1.33}{\mathrm{\Lambda }}^{3.11})$, $R^2=0.66$]. These results provide a theoretical basis for the prediction model of soil erosion on the slope and applies the theory of open-channel flow to overland flow.