The semi-empirical model for critical bed shear stress in the local scour hole downstream of a submerged structure based on turbulent velocity distribution

The investigation of the critical bed shear stress at the bed surface with negative slopes in the scour hole downstream of a submerged structure has primarily relied on experimental methods with limited theoretical exploration. This paper examined the distribution of near-bed flow velocity and turbulence intensity at the equilibrium stage based on physical model experiments of local scour downstream of a submerged weir. Additionally, the current study established equations for calculating the distribution of the near-bed mean flow velocity and relative turbulence intensity at the bed surface of the scour hole with negative slopes. Integrating mechanics, probability theory, and statistics introduced an impact force resulting from water flow on the local bed surface. Furthermore, a semi-empirical model for the dimensionless critical bed shear stress was developed applying this basis. The predicted values of the semi-empirical model were consistent with the measured values. They can be utilized to calculate the critical bed shear stress in the local scour hole downstream of the submerged weirs. The near-bed mean flow velocity and relative turbulence intensity introduced in the equation are key parameters that reflect the microscopic mechanisms on the local bed surface. Utilizing these microscopic parameters also avoids the influence of upstream structural configurations in the scour hole, thus broadening the applicability of the study's findings. This development not only deepens the understanding of velocity distribution patterns on the negative slope of the local scour hole downstream of submerged structures in rivers or the ocean but also offers a theoretical foundation for enhancing the precision of numerical models of local scour and for the application of critical standards of sediment initiation in related studies.