## 5 Conclusions  
The paper presents the results of a numerical study about the effect of junction angle on flow structure and transverse mixing at a confluence. Flow and mixing analyses in confluences were conducted under conditions of \(M_{r}=1.62\) and \(\alpha=30^{\circ}-90^{\circ}\) to analyze the storage effects caused by recirculation zones. In this study, the following results were obtained:  
* As the junction angle increases, the strength of helical motion and vorticity magnitude increase, leading to an increase in the vertical gradient of the mixing layer and mixing metric of the dosage curves.
* The recirculation zone creates a boundary layer that interrupts the inflow of solute and simultaneously accumulates solute. These storage effects of the recirculation zone generate long-tailed concentration curves, where the skewness significantly increases at junction angles of \(30^{\circ}\) to \(60^{\circ}\).  
Figure 17: Relationship between the transverse dispersion coefficient and mass exchange rate.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\alpha\) (\({}^{\circ}\)) & 90 & 75 & 60 & 45 & 30 \\ \hline \(T\) (s) & 77.52 & 76.34 & 73.53 & 71.94 & 50.76 \\ \hline \(A_{s}\) (m\({}^{2}\)) & 29.76 & 26.04 & 16.56 & 6.72 & 3.60 \\ \hline \(\varepsilon\) & 0.24 & 0.22 & 0.18 & 0.14 & 0.11 \\ \hline \(\varepsilon/T\) (s\({}^{-1}\)) & \(3.10\times 10^{-3}\) & \(2.88\times 10^{-3}\) & \(2.45\times 10^{-3}\) & \(1.95\times 10^{-3}\) & \(2.17\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Storage zone model parameters for recirculation zones in confluences for different junction angles.  
* The interaction between the helical motion and recirculation zone affects transverse mixing, where the transverse dispersion coefficient exhibits a positive correlation with the helical motion intensity and negative correlation with the recirculation zone size.
* The transverse dispersion coefficient has an inverse relationship with the mass exchange rate of the storage zone. Based on these results, it can be inferred that transverse dispersion is replaced by mixing due to strongly developed storage zones.  
The aforementioned analysis results are limited to the case of \(M_{r}=1.62\) and to the time-averaged flow field. Despite the properly reproduced flow simulation results, the solute mixing simulation results have limitations because the results were not completely validated using experimental results. Therefore, additional detailed research on solute and solids mixing due to the storage zone would require a mass exchange rate based on turbulence structures near recirculation zone boundaries.  
Conceptualization, J.S. and I.P.; methodology, I.P.; software, I.P.; validation, J.S., S.L. and I.P.; formal analysis, J.S.; investigation, J.S.; resources, I.P.; writing--original draft preparation, J.S. and I.P.; writing--review and editing, I.P.; visualization, S.L.; supervision, I.P.; project administration, I.P.; funding acquisition, I.P. All authors have read and agreed to the published version of the manuscript.  
This study was supported by the Korea Environment Industry & Technology Institute (KEITI) (2021003110003).  
Not applicable.  
The data presented in this study will be shared by the authors if requested.  
This work was supported by Korea Environment Industry & Technology Institute (KEITI) through the Measurement and Risk Assessment Program for Management of Microplastics Project, funded by Korea Ministry of Environment (MOE) (2021003110003).  
The authors declare no conflict of interest.