Theoretical Approach for Shear-Stress Estimation at 2D Equilibrium Scour Holes in Granular Material due to Subvertical Plunging Jets

The estimation of flow-induced shear stresses acting on the surface of scour holes still represents a challenge for scientists and engineers. From the practical point of view, excessive shear stresses can lead to significant scour depths, resulting eventually in the failure of the structure. From the scientific point of view, detailed knowledge of the shear stresses can yield novel insights for further understanding of scour in particular and of two-phase flows in general. Numerous studies have focused on the interaction between the water flow and a granular bed in order to furnish usable expressions for design and to provide knowledge of the erosive mechanisms. Most of those approaches are empirical, and are characterized by rather significant limitations due to tested conditions. Conversely, only a few studies have derived general theoretical equations for the prediction of the shear stresses based on the phenomenological theory of turbulence. To the best of the authors' knowledge, no works have taken into consideration the effect of the amount of suspended sediment on the value of the shear stress at the dynamic equilibrium configuration. This paper proposes a model based on the conservation of the angular momentum in the turbulent pothole to address those stresses. Novel experimental tests allowed for the validation of the derived equation, which is consistent with accepted theoretical and semitheoretical results.