Affinity and similarity of local scour holes at bed sills

Excessive erosion of gravel bed rivers represents a hazard, which is often controlled by the construction of bed sills. Shape and volume of equilibrium local scour holes at bed sills in high-gradient streams were investigated by analyzing steady flow experimental data. Scour profiles were normalized by scaling the depths and the longitudinal distance from the upstream sill with the maximum dimensions of the scour hole. Results exhibited a universal geometrical affinity of the scour. Geometrical similarity was also found to occur, but only in a limited range of physical conditions. Evidence on the scaling nature of the scour hole shapes has important implications on the prediction of the eroded volume. In turn, a correct evaluation of the eroded volume is necessary for the optimization of the design of the intersill distance. Prediction formulae are proposed which link the eroded volume to the geometrical, hydraulic, and sediment properties.