This numerical study of scour process tested the skills of computational fluid dynamics in modeling the unsteady flow field during the scour development stage by two-dimensional turbulent wall jets under a sluice gate. The modeling was found to well describe the experimentally observed flow patterns, that is, the main jet diverged to a returning jet and a tail jet. The model also correctly predicts the evolution of the scour depth and length. We examined the self-similarity of the profiles of scour bed and overlying velocities throughout the entire scour development and equilibrium stages. We found self-preserved profiles of velocities and scour beds using local jet parameters. Four growth curves were compared in describing the temporal evolution of scour depth. Finally, non-dimensional scaling of the equilibrium maximal scour depth was investigated. We used the theory of wall jet, and suggested that a modified jet Froude number can be used to predict the equilibrium scour depth, which accounts for the attenuation of the jet velocities along the apron.