A multi-phase SPH simulation of hydraulic jump oscillations and local scouring processes downstream of bed sills

In the present study, we numerically focus on the vorticity generation mechanism in a scour hole developed downstream of a grade control structure in sand-bed channels. The liquid-granular flow has been simulated through a symplectic Weakly Compressible SPH scheme with a two-equation turbulence model, where the two phases are treated as continua with different rheological properties. The equilibrium configuration of flow field and bed topography is reached after a transient period in which the system oscillates between two flow patterns: (i) the scour hole shows a relatively steep hump downstream of it, increasing the free surface elevation and generating a B-jump type with a counterclockwise rotating macro-vortex structure which pushes the main flow towards the bed, where strong erosive action is observed; (ii) the scour shows a relatively modest inclination of the scour cavity, leading to the formation of a wave jump dominated by a clockwise rotating macro-vortex structure.