Numerical investigation of scour on a sand bed induced by a moving vertical circular jet

This study employs three-dimensional numerical simulations to investigate scour development on a sand bed induced by a translating vertical circular jet. Simulations were performed for jet exit velocities from 2 to 4 m/s and nozzle translation speeds from 0.05 to 0.2 m/s. The results show that nozzle translation rapidly terminates local erosion at previous impingement locations, while the induced horizontal momentum enhances downstream bedload mobility and allows limited suspended sediment transport. Sediment transport evolves through four stages, and the scour geometry transitions from an initially circular cavity to a ribbon-like depression with a spoon-shaped transport zone. The scour pit exhibits three characteristic sections, including an initial section that grows rapidly with increasing exit velocities, a stable section with nearly constant width and length, and a developing section controlled by the downstream bedload transport range. Increasing exit velocities enlarges pit width but shortens the developing section, whereas increasing translation speeds reduces local peak shear while extending the downstream transport range. An empirical regression model is proposed to predict the stable-section pit width, and a hyperbolic function is used to estimate the maximum scour depth and pit width at the scour point. These findings clarify sediment transport behavior under translating jets and provide predictive tools for engineering applications.