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

Abstract

Periodic shock waves of roll waves may cause the flow to jump over the canal bank, increase soil erosion, and enhance the destructive power of debris flow. This paper focuses on the spatiotemporal changes in waveform, velocity, discharge, shear stress, and Froude number during the development process of roll waves, taking the non-uniform flow as the initial condition. This work studied numerically the influence mechanism of different variables on the development process of roll waves based on steep slope shallow water equations. The roll wave is unstable when the disturbance amplitude is too large. By reducing the inlet velocity, increasing the disturbance wavelength, and reducing the roughness coefficient, it can make the roll wave stable. Reducing the inlet velocity not only reduces the frequency of the shock wave but also keeps the wave crest from rising. Under different boundary conditions of disturbance amplitude, the crest growth rate (crest water depth difference/crest distance difference) of the roll wave development segment at a certain time is almost consistent. For different initial water depths, there is overlap in the roll wave development segment at a certain time. Under the initial condition of non-uniform flow, the congestion at the inlet means that the initial water depth is less than the normal water depth, and the decline of the water depth at the inlet means that the initial water depth is greater than the uniform water depth.