# Experiments on Longitudinal and Transverse Bedload Transport in Sine-Generated Meandering Channels
## 3 Results  
### The 110\({}^{\circ}\) Flume  
Figure 1(a) shows the bed elevation change (cm) in the sine-generated flume with deflection angle \(\theta_{0}=110^{\circ}\). Figure 1(b),c show the gain and loss of colored grains (D\({}_{1}\), D\({}_{2}\), D\({}_{3}\), and D\({}_{4}\)). The left panel shows the average of the two-dimensional flume with deflection angle \(\theta_{0}=110^{\circ}\). The right panel shows the average of the  
\(\text{D}_{3}\), and \(\text{D}_{4}\)) at each cross section along the left and right half-width parts of bends (using the channel centerline as the divider), respectively. The vertical axes in Figure 2b,c i.e., SV, display the sample volume (\(\text{m}^{3}\)) of colored grains, and positive and negative values indicate gain and loss, respectively. Figure 2: _Cont._  
Figure 2a shows the bed elevation change (cm) in the 110\({}^{\circ}\) flume. To trace bedload movement in various fluvial regimes, we designed a closed system for the 110\({}^{\circ}\) flume in this study, i.e., no sediment feed at the inlets. Since the bedload transport rates are relatively low and bed deformation is relatively mild in either B\({}_{1}\) or B\({}_{3}\), the intermediate scenario in B\({}_{2}\) can be considered to be in quasi-equilibrium. From Figure 2a, one can observe a continuous deposit along the convex bank (sections 41-57). Relatively severe scouring occurred near the apex sections 48-49 and the downstream of sections 55-57. For the 110\({}^{\circ}\) flume, sand grains of D\({}_{1}\) and D\({}_{2}\) are initially paved along the left (concave) and right (convex) bank of the B\({}_{1}\) bend (sections 13-37, as shown in Figure 1). The general bed topography shown in Figure 2a indicates the formation of alternate erosion/deposition areas whose localization along the bend is similar to that obtained by Termini (13, 19) in a meandering flume characterized by the same planimetric configuration as that of the 110\({}^{\circ}\) flume considered in this work. Figure 2b indicates a large quantity of D\({}_{1}\) grains (total volumes of 34.9 \(\times\) 10\({}^{-4}\) m\({}^{3}\)) were eroded from the left (concave) bank. Within the B\({}_{1}\) bend, most of those eroded D\({}_{1}\) grains (72%) were longitudinally transported to the next bend B\({}_{2}\) and only a small proportion (28%) crossed the channel centerline and contributed to the point bar deformation (as shown in Figure 2c). The evacuating amount of D\({}_{2}\) in the B\({}_{1}\) bend is relatively small (18.1 \(\times\) 10\({}^{-4}\) m\({}^{3}\)) compared to the scouring near the concave bank (about 52% in volume). About 86% of the D\({}_{2}\) grains eroded from the B\({}_{1}\) bend were longitudinally transported to the next bend B\({}_{2}\), i.e., the transverse transport of D\({}_{2}\) grains accounts for only 14% (as shown in Figure 2c). Therefore, in the B\({}_{1}\) bend of the 110\({}^{\circ}\) flume, bed degradation occurred, and the longitudinal bedload transport prevailed along both sides of the banks. As D\({}_{1}\) and D\({}_{2}\) grains moved into the next bend B\({}_{2}\) (sections 37-61, as shown in Figure 1), the longitudinal-transverse sorting continues. From Figure 2b,c, we measured the volumes of 15.9 \(\times\) 10\({}^{-4}\) m\({}^{3}\) and 11.3 \(\times\) 10\({}^{-4}\) m\({}^{3}\) of D\({}_{1}\) grains in the left (longitudinally transported) and right (transversely transported) half-width, respectively. The ratio of longitudinal to transverse transport for D\({}_{1}\) in the B\({}_{2}\) bend is about 1.4, while for D\({}_{2}\) grains, we measured the volumes of 2.0 \(\times\) 10\({}^{-4}\) m\({}^{3}\) and 5.0 \(\times\) 10\({}^{-4}\) m\({}^{3}\) in the right (longitudinally transported) and left (transversely transported) half-width, respectively. The ratio of longitudinal to transverse transport for D\({}_{2}\) in the B\({}_{2}\) bend is about 0.4. Figure 2: (**a**) Bed elevation change (Run 110/1, unit: cm, flow from left to right).