Numerical study of roll wave development for non-uniform initial conditions using steep slope shallow water equations

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The formation of roll waves in the spillway leads to the inability of the water flow to entrain air, which leads to the failure of the stilling basin to effectively dissipate energy, and the sudden increase in water depth will lead to the water flow jumping out of the embankment. For overland flow, the appearance of shock waves in roll waves can accelerate soil erosion. Roll waves occur not only in the aforementioned Newtonian fluid (water) but also in non-Newtonian fluids such as debris flows. Due to the occurrence of shock waves in the roll wave of debris flow, the debris flow in the roll wave state is more harmful than that in the non-roll wave state .Therefore, the study of roll waves has important scientific value and practical significance for many fields such as hydraulic engineering, geophysics, and disaster prevention and reduction. Therefore, based on the steep slope shallow water equation, this paper numerically analyzes the difference between the roll wave evolution process of the initial condition of uniform flow and non-uniform flow. Then, under the initial condition of non-uniform flow, the inlet boundary conditions such as disturbance amplitude, inlet velocity, disturbance wavelength, initial water depth, and topographic conditions such as roughness coefficient and slope are taken as variables. The temporal and spatial evolution of parameters such as waveform characteristics, Froude number, shear stress, velocity, discharge, wavelength, and crest growth rate under the influence of different variables during roll wave development is studied numerically, focusing on the dynamic process of roll wave development. The research results of this paper have important guiding significance for channel design, hillslope soil erosion prevention and control, and debris flow prevention and mitigation.

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