## 4 Discussion  
### Solute Mixing Downstream of Junction  
In this study, the effects of the junction angle on the mixing characteristics at the channel confluence and retention of the solute cloud in the storage zone were analyzed. First, the reproducibility of the flow pattern at the confluence was evaluated by changing the junction angle. Following the experimental research by [PERSON] et al. [38], the simulation results in this study also demonstrated that as the junction angle increases, the length and width of the recirculation zone increase. Additionally, the simulation results reproduced a clockwise helical cell, which was developed at the outer bank downstream of the confluence. Field measurements by [PERSON] and [PERSON] [54] revealed similar results, where one secondary cell developed downstream of the junction under the condition of \(M_{r}>1\). As the junction angle decreased, the center of the helical cell moved slowly toward the bottom of the channel (Figure 8) and showed similar results to [PERSON] et al. [23], where numerical simulations revealed a decrease in the \(u\) velocity. These previous studies verify the applicability and validity of the simulation results derived in this study.  
Previous studies have reported that transverse mixing is related to the momentum flux ratio (\(M_{r}\)). [PERSON] et al. [16] and [PERSON] and [PERSON] [41] reported that transverse mixing increases with \(M_{r}\). Additionally, the results presented by [PERSON] et al. [30] support the positive correlation between transverse mixing and \(M_{r}\) based on field measurements, where \(D_{T}/hu^{*}\) was \(1.34\), \(M_{r}=1.15\) and \(2.21\), and \(M_{r}=1.54\). However, analysis of the transverse dispersion associated with flow structures by junction angle has been limited in previous studies. In this research, simulation results demonstrated that transverse mixing depends on two main features: helical motion and recirculating flow. Therefore, the relationship between the two main flow features caused by the junction angle and transverse dispersion coefficients is presented in Figure 16. In Figure 16, \(D_{T}/hu^{*}\) is calculated using Equation (8), resulting in a range of \(0.32\)-\(0.82\). These results show that \(D_{T}/hu^{*}\) increases with the relative intensity of helical motion versus the \(u\) velocity \(\frac{1}{W}\int_{0}^{W}I\,dy/\overline{u}\), where \(\overline{u}\) is the depth-averaged \(u\) velocity (Figure 16a). In contrast, \(D_{T}/hu^{*}\) decreases with an increase in the length (Figure 16b) and width of the recirculation zone (Figure 16c). Since the recirculation zone size range sizes over flow depth, these results are valid for the recirculation zone size based on the depth-averaged flow field. As the junction angle increases, the helical motion intensity decreases because the increase in the \(u\) velocity was more dominant than that in the \(v\) velocity as a result of flow contraction caused by the occurrence of a recirculation zone. Therefore, one can see that the interrelationship between the helical motion and recirculation zone caused by a change in the junction angle affects transverse mixing.  
Figure 16: Cont.