Hydraulics of B-F and F jumps in adverse-slope stilling basins

Studies on the hydraulic jump on an adverse slope are limited because of its unstable configuration. However, both this hydraulic phenomenon (termed the F jump) and its extension (which begins on a positive slope and ends on a negative slope, termed the B-F jump) are encountered in practice and hence require greater examination. Experiments were conducted in a stilling basin of an ogee standard weir. The main characteristics of the jump, namely the sequent depth, the roller length and the energy loss were analysed. Using the momentum equation and experimental results, this paper derives semi-empirical and empirical relations for predicting the sequent depth ratio. An empirical expression is also provided to predict the roller length. Analysis of the results reveals that, as expected, a basin's adverse slope has a significant effect on the sequent depth ratio, roller length and relative energy loss. It was found that a positive slope increases the sequent depth as well as roller length, but decreases the relative energy loss. It was also noted that B-F jumps are much more stable than F jumps. The proposed relations in non-dimensional form and related analyses may assist in practical design of stilling basins on adverse sloping floors downstream of hydraulic structures.