# Experiments on Longitudinal and Transverse Bedload Transport in Sine-Generated Meandering Channels
## 3 Results
### The 30\({}^{\circ}\) Flume  
Figure 3a shows the bed elevation change (cm) in the sine-generated flume with the deflection angle \(\theta_{0}\) = 30\({}^{\circ}\). The most profound scouring-deposit was observed around the inflection points of the sine-generated curve rather than the apexes. Similar to Figure 2, Figure 3b,c show the gain and loss of colored grains (D\({}_{1}\), D\({}_{2}\), D\({}_{3}\), and D\({}_{4}\)) at each cross section along the left and right half-width of bends (using the channel centerline as the divider), respectively. The 30\({}^{\circ}\) flume is also a closed system in this study, i.e., no sediment feed at the inlets. Compared with the 110\({}^{\circ}\) flume, the channel slope for the 30\({}^{\circ}\) flume decreases from 2% to 1.12%; however, the inflow discharge increases from 50 to 60 m\({}^{3}\)/h, which results in a 15% increase in sectional-averaged velocity (see Table 1). For the 30\({}^{\circ}\) 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 5-13, as shown in Figure 1). Figure 3b indicates a quantity of D\({}_{1}\) grains (total volumes of 3.5 \(\times\) 10\({}^{-4}\) m\({}^{3}\)) were eroded from the left (concave) bank. Similar to the 110\({}^{\circ}\) flume, within the B\({}_{1}\) bend of the 30\({}^{\circ}\) flume, most of those eroded D\({}_{1}\) grains (71%) were longitudinally transported to the next bend B\({}_{2}\), and only a small proportion (29%) crossed the channel centerline and contributed to the B\({}_{1}\) bend point bar deformation (as shown in Figure 3c). Differing from the 110\({}^{\circ}\) flume, the evacuating amount of D\({}_{2}\) in the B\({}_{1}\) bend of the 30\({}^{\circ}\) flume is relatively large (5.5 \(\times\) 10\({}^{-4}\) m\({}^{3}\)) compared to the scouring near the concave bank (about 1.6 times in volume). For the 30\({}^{\circ}\) flume, about 90% 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 10% (as shown in Figure 3c). Similarly, in the B1 bend of the 30\({}^{\circ}\) flume, bed degradation occurred, and the longitudinal bedload transport prevailed along both sides of the banks. As D1 and D2 grains moved into the next bend B2 (section 13-21, as shown in Figure 1), the longitudinal-transverse sorting continues. As shown in Figure 3,c, we measured almost identical  
Figure 3: (a) Bed elevation change (units are cm, Run 30/1, flow from left to right). (b) Sample volume (unit: m\({}^{3}\)) of grains D1, D2, D3, D4 at each section along the left bank. (c) Sample volume (unit: m\({}^{3}\)) of grains D1, D2, D3, D4 at each section along the right bank. D1, D2, D3, D4 grains are represented by green, yellow, red, and cyan colors, respectively. volumes of 0.9 \(\times\) 10\({}^{-4}\) m\({}^{3}\) of D\({}_{1}\) grains for both the left (longitudinally transported) and right (transversely transported) half-width channel in the B\({}_{2}\) bend. In other words, the ratio of longitudinal to transverse transport for D\({}_{1}\) in the B\({}_{2}\) bend is about 1.0. For D\({}_{2}\) grains. We measured the volumes of 2.3 \(\times\) 10\({}^{-4}\) m\({}^{3}\) and 2.9 \(\times\) 10\({}^{-4}\) m\({}^{3}\) in the right (longitudinally transported) and left (transversely transported) half-width channel, respectively. The ratio of longitudinal to transverse transport for D\({}_{2}\) in the B\({}_{2}\) bend is about 0.8. Sand grains of D\({}_{3}\) and D\({}_{4}\) are initially paved along the left (convex) and right (concave) bank of the B\({}_{2}\) bend of the 30\({}^{\circ}\) flume (Figure 1). Figure 3b indicates a quantity of D\({}_{4}\) grains (total volumes of 3.1 \(\times\) 10\({}^{-4}\) m\({}^{3}\)) were eroded from the left (concave) bank.