LAUSR

A hydraulic jump is the rapid transition from a supercritical to subcritical flow. This transition is characterized by large-scale turbulence and energy dissipation. Despite the importance of understanding the hydraulic jump to design hydraulic structures, few studies have aimed on hydraulic jumps in U-shaped channels. In this paper, the 3D pattern of hydraulic jumps in U-shaped channels is studied numerically. The variations of the flow free surface are predicted using the volume of fluid scheme. Also, the flow field turbulence is simulated using the standard $$k-\varepsilon $$k-ε and RNG $$k-\varepsilon $$k-ε turbulence models. According to the numerical modeling results, the standard $$k-\varepsilon $$k-ε turbulence model estimates the flow characteristics with more accuracy. A comparison between the laboratory and numerical results shows that the numerical model simulates the flow field characteristics with good accuracy. For example, in the hydraulic jump model with a relative discharge $$({q=Q/{\sqrt{( {gD^{5}})}}})$$(q=Q/(gD5)) equal to 0.321 and a Froude number $$({{F}_1})$$(F1) equal to 4.85, the values of MAPE, RMSE and $${R}^{2}$$R2 are calculated 7.617, 0.022 and 0.989, respectively. Next, 45 numerical models are simulated in different hydraulic conditions and some relationships are provided for calculating the sequent depth $$({{h_2 }/{h_1 }})$$(h2/h1), hydraulic length $$({{L_\mathrm{j}}/{h_1}})$$(Lj/h1) and roller length $$({{L_\mathrm{r} }/{h_1}})$$(Lr/h1) ratios by analyzing their results.