## 5 Analysis of Simulation Results
### Vorticity  
The vorticity distribution in a flow field reflects the distribution of vortex cluster occurrence and flow separation intensity in that field. Figure 14 illustrates vorticity along each section. The figure shows that the vorticity of the straight sections of the bend is low but increases in the bend sections. The vorticity at the convex bank is higher at both sides of the bend and at the water surface, especially near section D90. After entering the bend, the centrifugal stress readjusts the water flow structure, making the surface water flow move toward the convex bank, thereby increasing its velocity gradient and vorticity. After crossing the D90 bend section, the water flow moves gradually to the concave bank. Momentarily, water separation occurs near the convex bank, making the vorticity increase rapidly and the vorticity distribution area expand intensely.  
Figure 13: The distributions of bed shear stress of bend.  
As with Figure 9, the circulation strongly correlates with the vorticity distribution: the circulation intensity is complex, and the vorticity distribution is large. Figure 8 illustrates the location of the complex circulation and the corresponding large vorticity of each section. After the bend, the concave bank vorticity enlarges. After exiting the bend, the convex bank vorticity enlarges, as illustrated in Figure 8. The velocity gradient near the convex bank of the straight exit sections of the bend changes significantly. Figure 12 also shows that the circulation is near the convex bank of the straight exit sections of the bend, which causes large vorticity.  
Figure 15 illustrates vorticity distributions at different water depths. The surface vorticity is evenly distributed and large because the shear stress between the surface water flow and air increases the flow velocity gradient. Figure 15a,b show that the vorticity distribution is extremely uneven and concentrated in the narrow area of the convex and concave banks of the bend with a high vorticity intensity. Near the top of the bend, the vorticity intensity is greatest but significantly reduced at the middle of the bend. The vorticity intensity distribution of the concentrated zone is 10 times higher than that in the weak distribution zone. The phenomenon can be explained as follows. First, in the longitudinal flow of the flume, the water flow is separated at the corner of the rectangular sections, and the separation point is the origin of the vortex cluster having strong vorticity. Second, near the top of the bend, the cross-sectional circulation causes a strong water separation at the corner of the top sections of the bend, creating a strong vortex, which is reflected in the concentrated strong-vorticity area. Third, after passing the top of the bend, the cross-sectional circulation causes the water flow mainstream to gradually shift from the convex bank to the concave bank, increasing the size of the water separation area at the convex bank and enlarging the strong-vorticity distribution area. Figure 15b shows that the strong-vorticity distribution area of the concave and convex banks at the water surface is large. This is because as the water flow mainstream gradually moves from the convex bank to the concave bank, the separation area first enlarges and then shrinks along the water depth near the convex bank. The separation area near \(z/H=0.5\) is larger, as shown in Figures 8 and 9.  
Figure 14: Vorticity diagram along the cross section.