SPH modelling of hydraulic jump at high Froude numbers at an abrupt drop: vorticity and turbulent pressure fluctuations

This paper numerically investigates the physical features of hydraulic jump oscillations at an abrupt drop with high Froude numbers reaching values up to 9.92. In order to emphasize the importance of the bottom shape, different relative step heights in the range between 0.9 and 3.4 have been analysed, leading to the occurrence of different jump regimes (A-wave, A-jump, B-wave and B-jump). For the case of the B-jump type, the jump toe is drifted downstream when the Froude number increases. For the A-jump type with high Froude, the surface roller is made up of an increasing several number of vortices and thus the jump toe is drifted upstream, when the Froude number increases. In particular, for the case of the A-jump type at the highest simulated Froude number, when the toe of the jump is at its most upstream location, the maximum number of anticlockwise vortices (with decreasing sizes) is observed. At the same time, the turbulence levels decrease much faster due to the dominance of viscous forces at the small scales. Instead, when the toe of the jump is moving downstream, the neighbouring vortices tend to influence each other with their rotation and to coalesce into one larger vortex and the turbulence levels increase rapidly due to the dominance of inertial forces. A statistical analysis indicates that turbulent pressure fluctuations increase rapidly from the toe of the jump and reach a peak in the roller region, downstream of which they decrease again. The structure of the turbulent pressure fluctuations depends on the Froude number.