Numerical Study of Roll Wave Characteristics Based on Navier-Stokes Equations: A Two-Dimensional Simulation

Roll waves are frequently observed in the spillway chutes of hydropower stations, flood discharge channels, and diversion canals. In order to understand the physical characteristics of roll waves in detail, a full two-dimensional numerical model based on the Reynolds-averaged Navier-Stokes equation with the renormalized group k-ϵ turbulence model and a volume of fluid technique is established to simulate the evolution of the roll wave. A series of periodic roll waves generated by different combinations of slopes and discharges is successfully simulated, which compares well with the famous Brock's roll wave experiments. Compared with the traditional study by the Saint-Venant equations, the distribution characteristics of roll waves, such as flow velocity and turbulent kinetic energy, are obtained. Simulated results show that the turbulent effect is not evenly distributed and may play an important role in roll wave generation and evolution. Further, an additional parameter examination shows the roll wave amplitude ratio and wave speed decrease with the increase of the fluid viscosity. These detailed flow structures of roll waves might be helpful in understanding the physical mechanism of roll waves and the spillway design and bed erosion study.