Scaling laws for two- and three-dimensional wall jet scour based on the phenomenological theory of turbulence

The scour induced by wall jets may cause serious bed erosion and thus damage to hydraulic structures. Previous studies are largely empirical, providing only correlations of experimental data. At present, it is not clear what difference exists in the physical mechanisms of two-dimensional (2D) and three-dimensional (3D) wall jet scour. This study first summarizes previous efforts for predicting wall jet scour depths. Then, a scaling analysis is presented for investigating scour depths by applying the phenomenological theory of turbulence. It is shown that for wall jet cases, the dimensionless equilibrium scour depth can generally be expressed as a power function of the densimetric Froude number and relative roughness height, with the power index depending on jet configurations. The predictions of scour depth using the resulting formulas agree well with published data. The present analysis provides new insights into the understanding of the underlying physical mechanisms of wall jet scour as well as the difference between 2D and 3D configurations.