Roll waves in overland flow

Roll waves are frequently observed in overland flow, especially in rill flow, which has an important effect on the development of soil erosion. Using one-dimensional St. Venant equations, this paper investigates the dynamics of periodic roll waves based on Dressler's and Brock's work. Under the assumption that the average flow depth equals the uniform flow depth, expressions of the roll-wave speed and roll-wave profile were obtained. Testing with the results observed by Brock in 1970 for wave properties shows that these expressions can approximately describe the characteristics of periodic permanent roll waves. Numerical solutions of roll waves under specific conditions are found. They show that when a roll wave appears, the shear stress of flow increases, and soil erosion accelerates.