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.

本文通过数值研究了弗劳德数高达 9.92 的突然下降时水跃振荡的物理特征。为了强调底部形状的重要性，分析了 0.9 和 3.4 之间范围内的不同相对台阶高度，导致出现不同的跳跃状态（A 波、A 跳跃、B 波和 B 跳跃） ). 对于 B 跳类型的情况，当弗劳德数增加时，跳趾向下游漂移。对于高弗劳德的A跳型，当弗劳德数增加时，表面滚筒由越来越多的涡流组成，因此跳趾向上游漂移。特别地，对于最高模拟弗劳德数的 A 跳类型，当跳跃的脚趾位于其最上游位置时，观察到最大数量的逆时针涡流（尺寸减小）。同时，由于粘性力在小尺度上占主导地位，湍流水平下降得更快。相反，当跳跃的脚趾向下游移动时，相邻的涡流倾向于通过旋转相互影响并合并成一个更大的涡流，并且由于惯性力的主导，湍流水平迅速增加。统计分析表明，湍流压力波动从跳跃的脚趾处迅速增加，并在滚筒区域达到峰值，然后在下游再次减小。湍流压力波动的结构取决于弗劳德数。由于粘性力在小尺度上占主导地位，湍流水平下降得更快。相反，当跳跃的脚趾向下游移动时，相邻的涡流倾向于通过旋转相互影响并合并成一个更大的涡流，并且由于惯性力的主导，湍流水平迅速增加。统计分析表明，湍流压力波动从跳跃的脚趾处迅速增加，并在滚筒区域达到峰值，然后在下游再次减小。湍流压力波动的结构取决于弗劳德数。由于粘性力在小尺度上占主导地位，湍流水平下降得更快。相反，当跳跃的脚趾向下游移动时，相邻的涡流倾向于通过旋转相互影响并合并成一个更大的涡流，并且由于惯性力的主导，湍流水平迅速增加。统计分析表明，湍流压力波动从跳跃的脚趾处迅速增加，并在滚筒区域达到峰值，然后在下游再次减小。湍流压力波动的结构取决于弗劳德数。相邻的涡流往往会通过旋转相互影响并合并成一个更大的涡流，并且由于惯性力的主导，湍流水平迅速增加。统计分析表明，湍流压力波动从跳跃的脚趾处迅速增加，并在滚筒区域达到峰值，然后在下游再次减小。湍流压力波动的结构取决于弗劳德数。相邻的涡流往往会通过旋转相互影响并合并成一个更大的涡流，并且由于惯性力的主导，湍流水平迅速增加。统计分析表明，湍流压力波动从跳跃的脚趾处迅速增加，并在滚筒区域达到峰值，然后在下游再次减小。湍流压力波动的结构取决于弗劳德数。