## 3 Results and Discussion
### Solute Transport and Dispersion
Thus, the difference in the BTC shape among the turbulence models is purely driven by the difference in the shear flow effects determined by the transverse gradients of the mean velocity, as shown in Figure 10a. In S157, meanwhile, the \(k-\omega\) and SST \(k-\omega\) models reproduce the flow separation in the vicinity of the outer bank (Figure 6a). This separated flow traps solute particles to the outer bank via the recirculating flows, then enhance the late-time tailing, as demonstrated in Figure 10b. As a result, the remarkable change in the BTC parameters between S136 and S157 is observed with the \(k-\omega\) and SST \(k-\omega\) models due to the trapping effects of the flow separation. More specifically, the SST \(k-\omega\) model exhibits that the absolute value of the power-law slope, and truncation time of S157 are about half and twice the values of S136, respectively (Table 2). On the other hand, the \(k-\varepsilon\) model fails to predict the onset of the flow separation for S157. The absence of the trapping effects caused by the flow separation induces the minor difference in the BTC shape between S136 and S157 with the \(k-\varepsilon\) model (Figure 9a,b). In S190, the onset of the separated recirculating flows is successfully simulated with all turbulence models even though the size of the recirculation zone varies with the turbulence models (Figure 6b). As a consequence, the \(k-\varepsilon\) model shows the sudden change in the BTC shape between S157 and S190, wherein the absolute value of the power-law slope, and truncation time of S190 are about one-third and twice the values of S157, respectively (Table 2). Moreover, the discrepancy in the power-law slope among the turbulence models is considerably reduced in S190. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**S136**} & \multicolumn{2}{c}{**S157**} & \multicolumn{2}{c}{**S190**} \\  & **Tail Power-Law** & **Truncation** & **Tail Power-Law** & **Truncation** & **Tail Power-Law** & **Truncation** \\  & **Slope** & **Time** & **Slope** & **Time** & **Slope** & **Time** \\ \hline \(k-\varepsilon\) & –27.84 & 1.49 & –16.25 & 1.81 & –4.66 & 3.54 \\ \(k-\omega\) & –15.28 & 2.20 & –7.68 & 3.19 & –3.77 & 4.85 \\ SST & –14.21 & 2.29 & –6.01 & 4.30 & –3.06 & 6.32 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Key parameters of breakthrough curves to evaluate the impact of turbulence models on tailing behaviors of solute particle spreading. Figure 9: Impact of turbulence models on 1D breakthrough curves of (**a**) S136, (**b**) S157, and (**c**) S190. According to Table 2, the simulation cases involving the recirculating flows commonly have truncation times larger than 3. This result implies that this truncation time value can be suggested as the threshold for identifying the non-Fickian transport signature ascribed to the flow separation in the meandering channels of this study. Nevertheless, the \(k-\varepsilon\) and \(k-\omega\) models exhibit the smaller truncation times and steeper power-law slopes than those of the SST \(k-\omega\) model. As previously discussed, this is because the reattachment length, width, and velocity magnitude of the recirculation zones differ by different turbulence models. Compared to the \(k-\varepsilon\) and \(k-\omega\) models, the SST \(k-\omega\) reproduces the larger and faster recirculating flows (Figures 6 and 7), and thus exacerbates the late-time tailing of the BTCs (Figure 9) owing to the stronger storage (trapping) effects on solute transport, as visualized in Figure 10c. Furthermore, the enhanced secondary flows simulated with the SST \(k-\omega\) model (Figure 5b) may promote the trapping effects by vigorously conveying solute particles to the flow separation zones near the outer bank via the transverse dispersion.