## 3 Results and Discussion
### Separated Recirculating Flows  
The high sinuosity causes the transverse gradient of the streamwise velocity biased largely toward the inner bank. This strong velocity gradient in the transverse direction forms the low-velocity zones near the outer bank, where it is notable that the negative streamwise velocity (backflow) is simulated at the bend apex with the SST \(k-\omega\) model for S190, as shown in Figure 5a. From the backflow, it is evident that horizontal recirculating flows take place in the vicinity of the outer bank owing to the adverse pressure gradients associated with the sharp bend curvature. At high sinuosity, the streamwise velocity structures are substantially influenced by the turbulence models (Figure 5a). Thus, it can be inferred that the turbulence models may directly affect the recirculating flow characteristics. Figure 6 shows that the separated recirculation zones emerge near the outer bank of the bend inlet in high-sinusosity cases of S157 and S190, as shown in Figure 6. [PERSON] (2018) revealed that the onset of the horizontal flow separation occurs at a specific level of the curvature ratio to channel width, \(R_{c}/W\leq 2\), which is consistent with \(R_{c}/W\) of S157 and S190, as presented in Table 1. According to Figure 6, however, the onset and size of the recirculation zones highly depend on the turbulence models. In S157, the \(k-\omega\) and SST \(k-\omega\) models adequately reproduce the onset of the recirculating flows, while the \(k-\varepsilon\) model fails to simulate the flow separation. In S190, all turbulence models are successful in reproducing the separated recirculating flows. Nevertheless, the \(k-\varepsilon\) and \(k-\omega\) models unpredict the reattachment length of the flow separation for both S157 and S190 compared to the SST \(k-\omega\) model (Figure 6). Figure 5: Influence of turbulence models on distributions of (**a**) depth-averaged streamwise velocity and (**b**) width-averaged spanwise velocity at the bend apex for S136 and S190. The insets indicate streamwise and spanwise velocity distributions of the SST \(k-\omega\) model, as a function of sinuosity. The influence of the turbulence models on the flow separation is further examined using its width and velocity magnitude. The transverse distributions of the depth-averaged mean velocity at the cross-section across the center of the recirculation zones is plotted in Figure 7. With this figure, the width of the recirculation zones is implicitly estimated by measuring the distance between the center of the recirculation zone and the wall. Please note that this study assumes the minimum-velocity point other than the near-wall boundary as the center of the recirculation zone, as illustrated in Figure 7b. In S136, no flow recirculation is simulated with all turbulence models as the minimum velocity occurs very near the wall, as shown in Figure 7a. For S157 and S190, the SST \(k-\omega\) model reproduces the faster and wider recirculating flows than those of other turbulence models, as depicted in Figure 7b,c. Particularly in S157, the \(k-\varepsilon\) model simulates the width of the recirculation zone close to zero, which indicates no occurrence of the flow separation (Figure 7b). These trends are consistent with the findings from Figure 6.  
In the meandering channel studied in this work, the extent of the separated flow recirculation would be critical in quantifying the magnitude of the non-Fickian transport because the larger recirculation zones trap more solute particles and directly contribute to longer residence times of  
Figure 6: Streamlines of velocity fields for (**a**) S157 and (**b**) S190, simulated with different turbulence models. \(L_{R}\) indicates the reattachment length of recirculation zones. Figure 7: Distributions of depth-averaged mean velocity at the cross-section crossing the center of recirculation zones for (**a**) S136, (**b**) S157, and (**c**) S190. The insets plot the distributions with the logarithmic scale on \(y\)-axis. solutes.