## 5 Analysis of Simulation Results
### Transverse Circulation
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Author** & \begin{tabular}{c} **Diameter-Width** \\ **Ration** \\ \end{tabular} & \
\begin{tabular}{c} **Breadth-Depth** \\ **Ratio** \\ \end{tabular} & **Froude Number** & **Central Angle** &
\begin{tabular}{c} **Position of Maximum** \\ **Circulation Intensity** \\ \end{tabular} \\ \hline [PERSON] [35] & 3 & 2.67/2.60/0.58 & 0.15/0.19/0.195 & 180\({}^{\circ}\) & 60\({}^{\circ}\) \\ [PERSON] [25] & 2 & 5 & 0.34 & 180\({}^{\circ}\) & 60\({}^{\circ}\) \\ This paper & 2 & 2 & 0.28 & 180\({}^{\circ}\) & 60\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Locations of the maximum circulation strength corresponding to different parameters. circulation occurs at the bottom of the water, and a clockwise circulation occurs in the concave bank at the water surface. The counterclockwise circulation near the convex bank at section D45 develops into a double-vortex counterclockwise circulation, resulting in the formation of many small circulations near the convex and concave banks. Figure 12: Flow chart of sections: (**a**) Q0.5; (**b**) Q0.8; (**c**) D30; (**d**) D45; (**e**) D60; (**f**) D90; (**g**) D135; (**h**) D180; (**i**) H0.5; (**j**) H0.8. When bending degree increases, circulations develop and turbulence intensifies, resulting in greater energy loss. At section D180, the water body at the surface flows smoothly, while the lower part of the water body circulates, especially near the concave bank. At the straight sections of the bend, the flow is still affected by the upstream bend; hence, the circulation continues at a reduced strength. Figure 12i,j illustrate the straight sections of the bend. The circulation remains, but a comparison of the circulation characteristics of each section in the bend shows that the circulation strength weakens. LES simulated the secondary flow structure of the cross section more accurately than the k-\(\varepsilon\) model. This reflects the benefits of applying the LES to studying curved open channel flows, which is consistent with the investigation of [PERSON] [4]. Shear stress is an important parameter to predict the degree of scour of the moving bed, and its distribution directly determines the scour form of the bed surface. Figure 13 shows the distribution of the shear stress on the bed surface at the bend. After the water flow enters the bend, the shear stress it receives begins to increase. The shear stress that the concave bank side receives is larger than the convex counterpart. The maximum shear stress appears before the top section of the curve, and it moves from the concave bank to the convex bank along the longitudinal direction of the curve, and the shear stress in the second half of the curve is smaller than that in the first half. After passing through the curved top section, the shear stress on the bed surface presents an opposite distribution characteristic to that before the curved top section, and its value at the convex bank is larger than that at the concave bank. According to the change of the curve circulation in the whole curve, it can be known that the turbulent shear stress and the curve circulation influence each other.