Theoretical investigation of dam-break waves in frictional channels with power-law sections

Abstract

Both the hydraulic resistance and the channel cross-sectional geometry have significant effect on the propagation of the dam-break waves. Analytical models including either of them have been available. However, it is not feasible to assess the comprehensive influence using the existing solutions. The present study considers a resistance-dominated wave tip region followed by an ideal fluid flow region in a dry horizontal channel whose cross-sectional shape is controlled by a power-law index n. Laboratory experiments and numerical simulations are conducted to measure/predict the water surface profiles of the dam-break flows in five types of flumes. The water depth, location and celerities of the wave front predicted by the analytical model agree well with the experimental and numerical results. The quantitative effects of the bottom resistance and the channel cross-sectional shape on the wave properties are investigated. Results show that the spatio-temporal variation in the wave feature of the dam-break flows strongly depends on the channel cross-sectional geometry; while the retardation effect of the bottom resistance becomes more significant as n increases. Furthermore, the derived analytic solution as well as the experimental data can be used for evaluating numerical solutions considering the hydraulic resistance and cross-sectional geometry.