## 3 Results and Discussion  
### Velocity Distributions  
This study explores 3D flow structures in meandering channels under the three different conditions of sinuosity. Figure 3 shows the mean velocity and turbulent kinetic energy (TKE) distributions simulated at the free surface with the SST \(k-\omega\) model. In this figure, the mean velocity distributions exhibit that the maximum velocity develops near the inner bank due to the centrifugal force, while the minimum velocity evolves along the outer bank. This trend is contradictory to the velocity distribution in natural rivers because the generated channels have the flat and smooth bed [56; 59]. In nature, rivers generally present the highest velocity along the outer bank because of sediment erosion and deposition. The significant velocity gradients in the transverse direction around the inlet of the meander bend increase TKE near the bend outlet because of a strong momentum transfer between the inner bank and the outer bank. As sinuosity increases, the discrepancy between the maximum inner-bank velocity and the minimum outer-bank velocity increases. Compared to S136 and S157, consequently, S190 exhibits the stronger velocity gradients across the channel width, which drive the higher level of TKE adjacent to the bend apex, as shown in Figure 3.  
Figure 2: Comparison between observation of [PERSON]’s experiments and simulations with three turbulence models: (**a**) streamwise velocity profiles and (**b**) spanwise velocity profiles. \(y/W\) and \(z/H\) denote the dimensionless distance from the left bank and channel bed, respectively. The momentum transfer within the meander bend is realized by the secondary flow. With the helical motion of the secondary flows, the high momentum fluid near the water surface transports toward the outer bank, whereas the low momentum fluid near the channel bed moves to the inner bank. The simulation results adequately reproduce these cross-sectional flow patterns, as depicted in Figure 4, in which the spanwise velocity vectors are overlain with the mean velocity distributions at the bend apex, simulated with three turbulence models under the different sinuosity conditions. This figure clearly shows that the secondary flow intensity is enhanced with increasing sinuosity, which also leads to an increase and a decrease in the velocity magnitude near the inner bank and the outer bank, respectively. All turbulence models used in this study successfully simulate the aforementioned helical secondary flows at the bend apex. Even if the entire flow features are consistent over all turbulence models, the SST \(k-\omega\) model reproduces the stronger intensity of the secondary flow than that of the \(k-\varepsilon\) and \(k-\omega\) models. Hence, the velocity near the water surface and channel bed, simulated with the SST \(k-\omega\) model, are higher than that of other turbulence models. The influence of the turbulence models on the flow simulations is investigated more rigorously using the depth-averaged streamwise velocity and width-averaged spanwise velocity profiles, as shown in Figure 5. From this figure, one can notice that the shear flows become stronger in both lateral and vertical directions as sinuosity increases. Although the topological characteristics exert a dominant control over the overall flow patterns in meandering channels, the detailed flow behaviors are governed  
Figure 4: Cross-sectional distributions of mean velocity with secondary flows at the bend apex for simulation cases with three different turbulence models. Figure 3: Mean velocity and turbulence fields at the free surface of a representative domain including the bend apex for simulation cases calculated with the SST \(k-\omega\) model. by the turbulence models. In S136, the velocity profiles are barely sensitive to the turbulence models. In S190, in contrast, the SST \(k-\omega\) model simulates the larger deviations in both the streamwise and spanwise velocity profiles than those of other turbulence models.