Analytical approach for predicting local scour downstream of submerged sluice gate with an apron

A new analytical method was evaluated for predicting scour profile downstream of a submerged sluice gate with an apron. The differential equations between bed Shear stress and Scour profile Curvature (SSC model) were utilized to predict the scour profile in both temporal and equilibrium stages. A jet momentum flux was considered as an external source of erosion on a hypothetical particle ring as the boundary between the flow and sediment bed. The scour length and sediment resistance factor were the two unknowns in the governing differential equations. Two solution strategies were introduced to provide a closed-form solution by using the prediction equations of maximum scour depth from the literature and by employing the von Kármán momentum integral equation. The first strategy was used to investigate the effect of jet angle of attack and the angle of the maximum scour slope on the prediction of scour profile. A sensitivity analysis was performed to determine an acceptable range for the maximum scour slope. The shear stress at the location of maximum scour was also estimated using the von Kármán momentum integral equation and the model was modified for erodible curved beds. The modified von Kármán equation was linked with SSC equations to predict the characteristic lengths of scour in temporal and equilibrium stages. Variations in bed shear stress at the location of maximum scour depth decreased non-linearly with time and reached the sediment critical shear stress at equilibrium. Four hydrodynamic regimes were classified to define the temporal variations of bed shear stress. The maximum error for prediction of scour profile with time occurred at the beginning of scour and the proposed model overestimated the maximum scour depth by 34.8% and underestimated the scour length by 7.6%.