Predicting the sequent depth ratio of a B-F hydraulic jump on a river-bed rock chute

Rock chutes are widely used to control erosion of river beds because of their high energy loss, low environmental impact, simple construction and low cost. They typically include a negatively sloped stilling basin, which leads to formation of a little-understood ‘B-F’ hydraulic jump. This has its toe located on the upstream positive slope of the chute and its roller length ending on the downstream negative slope of the stilling basin. In this study, a general equation for computing the sequent depth ratio of a B-F jump was developed using Buckingham dimensional analysis and the incomplete self-similarity theorem. A new non-dimensional parameter, E₀, including the effects of the jump toe and the location of the end of the roller length, was introduced. Laboratory experiments of B-F hydraulic jumps were conducted for a wide range of upstream Froude numbers, relative bed roughness, three different upstream channel slopes and three different negative downstream channel slopes. The sequent depth ratio on rough rocky beds was found to be considerably smaller than those on a smooth concrete bed. Two new prediction equations, for smooth and rough bed slopes, are presented and the results show that the predictions agree reasonably well with the experimental data.