Prediction of time-dependent local scour by impinging jets using a semi-analytical model

ABSTRACT

The main objective of this study was to investigate the evolution of local scour downstream of vertical impinging jets under clear-water conditions and to develop predictive models for both temporal scour development and equilibrium scour depth over uniform and non-uniform sediment beds. Through laboratory experiments, the temporal development of scour depth and scour profiles was monitored, while the influence of jet characteristics (velocity, drop height, and diameter), sediment properties (median diameter and gradation), and hydraulic parameters (tailwater depth) was examined. Results revealed a rapid initial scour phase followed by a gradual approach to equilibrium, with non-uniform sediments exhibiting reduced scour due to particle interlocking and bed stabilization. A semi-analytical model, derived from the sediment continuity equation and a pickup function, was proposed to predict time-dependent scour depth with an average deviation of about 7% from the experimental data, outperforming existing empirical models. Moreover, normalized scour profiles showed geometric similarity over time, as represented by a polynomial function. This study introduces a gradation parameter and a refined densimetric Froude number, improving prediction accuracy for non-uniform beds. These findings provide useful insight for the design of hydraulic structures exposed to jet-induced scour. Compared with previous formulas, the semi-analytical model reduced the mean relative error in predicting equilibrium and time-dependent scour depth by approximately 32% and 41%, respectively, demonstrating superior accuracy across different sediment gradations and hydraulic conditions.