Scour due to submerged planar wall jets: a model

In this study, equilibrium scour formed by submerged planar turbulent wall jets over a sediment bed is modeled. The theoretical framework consists of a flow model coupled with an equilibrium scour model. Using existing experimental data, a single-layer, self-similar velocity profile for submerged wall jets is proposed. This velocity profile, along with fluid continuity and momentum equations, enables the prediction of Reynolds shear stress and bed shear stress. The equilibrium scour model is developed by balancing the applied bed shear stress with the threshold bed shear stress required for the entrainment of sediment grains. By coupling the flow model with the scour model, equilibrium scour profiles are derived. As the jet progresses downstream, the redistribution of momentum leads to a reduction in both Reynolds shear stress and bed shear stress. The resulting equilibrium scour profile depends on three key parameters: the jet Reynolds number, dimensionless grain size, and scour coefficient. Characteristic lengths of the scour profile, such as the location of equilibrium scour depth, location of downstream dune crest, equilibrium scour hole length, equilibrium scour depth, and downstream dune height, increase and decrease, respectively, as the jet Reynolds number and dimensionless grain size increase. The location of equilibrium scour depth shifts toward the jet source with an increase in scour coefficient, which also leads to amplify the equilibrium scour hole length, equilibrium scour depth, and downstream dune height. The predictions from the present formulation show good agreement with existing experimental data and are consistent with Dey–Ali’s law for planar wall-jet scour.