Scaling laws of turbulent wall-jet scour: Planar and circular wall jets

A turbulent wall jet issuing tangentially over a loose sediment bed induces significant erosion, leading to the development of a scour hole. This perspective article presents a generalized scaling framework for determining the equilibrium scour depths caused by planar and circular wall jets. It applies the concept of similarity, including an incomplete similarity in the power-law asymptotic function of particle size to scour depth ratio. This framework demonstrates that the similarity exponent can be exclusively determined through the phenomenological theory of turbulence. The scaling laws reveal that the nondimensional scour depth obeys a linear-law with the respective planar and circular wall-jet scour numbers, which depend on issuing jet size, jet velocity, bed particle size, and threshold shear velocity. Moreover, the analysis reveals that for a given jet thickness equal to the jet diameter, the circular wall-jet scour number scales with the 3/5 power of the planar wall-jet scour number. The approach is extensively validated with the experimental data over a range of key parameters. The scaling laws provide valuable insights into the relationship between nondimensional scour depth and key hydrodynamic forces, including inertia, particle drag, shear, and threshold shear forces.