Hydraulic Jumps on Corrugated Beds

The results of a laboratory study of hydraulic jumps on corrugated beds are presented. Experiments were performed for a range of Froude numbers from 4 to 10. Three values of the relative roughness $t/y_1$ of 0.50, 0.43, and 0.25 were studied. It was found that the tailwater depth required to form a jump was appreciably smaller than that for the corresponding jumps on smooth beds. Further, the length of the jumps was about half of those on smooth beds. The integrated bed shear stress on the corrugated bed was about 10 times that on smooth beds. The axial velocity profiles at different sections in the jump were found to be similar, with some differences from the profile of the simple plane wall jet. The maximum velocity $u_m$ at any section in terms of the velocity $U_1$ of the supercritical stream was correlated with the longitudinal distance x in terms of L, which is the distance where $u_m=0.5U_1\text{,}$ and this relation was the same as that for jumps on smooth beds with the difference that $L/y_1$ was much smaller for jumps on corrugated beds. The normalized boundary layer thickness $\delta /b\text{,}$ where b is the length scale of the velocity profile, was equal to 0.45 for jumps on corrugated beds compared to 0.16 for the simple wall jet. The results of this study show the attractiveness of corrugated beds for energy dissipation below hydraulic structures.