# Experiments on Longitudinal and Transverse Bedload Transport in Sine-Generated Meandering Channels
## 4 Implication and Discussion  
The above analyses are based on our well-controlled flume experiments, in which both the channel width and the flow discharge are constant. Although channel widening or narrowing is common in fluvial rivers, countless aerial and satellite views indicate a relatively constant width prevails in a meandering channel with high sinuosity. In addition, bed deformation is related more to the bankfull discharge or the equivalent effective discharge. Therefore, it is reasonable to maintain steady and uniform flow in our experiments.  
The observed behavior of moving grains in Zone 1 (foreside of the point bars) and in Zone 2 (near the concave bank downstream of the bend apexes) is in agreement with what was observed by [PERSON] [18], when she performed an order-of-magnitude analysis of the momentum equation terms with data collected in a meandering laboratory flume having similar general bed topography and same planimetric configuration as the 110\({}^{\circ}\) flume used in the present work. [PERSON] [18] observed the existence of a good correspondence between the regions of outward direction of the bed shear stress and the regions of deposition. On the other side, [PERSON] [18] also verified that there is a strong interdependence between the downstream velocity and bed shear stress non-uniformity along the channel and the cross-circulation momentum transport, whose entity depends on the channel's curvature and on the aspect ratio. She verified the relative importance of the convective and the circulation motions with respect to the distribution of the bed shear stress, which determines the sediment transport along the channel. By comparing the map of positive/negative ratio of the downstream and the cross-stream components of the bed shear stress (which indicates the deviation of the bed shear stress vector from the downstream direction) along a bend with that of the erosion/deposition zones, she observed a good correspondence between the regions of outward direction of the bed shear stress and the regions of deposition. The strong mutual interaction between the cross-circulation and the downstream velocity affects not only the downstream component of the bed shear stress but also the transverse one and, consequently, the direction of the bed shear stress vector. As the curvature increases, the convective accelerations also increase, and the downstream velocity and the bed shear stress, are forced towards the outer bank; as a result, the bed shear stress decreases along the inner bank and increases along the outer bank. Based on her experimental results, she observed that the combination of forces along the bend causes the bed shear stress to shift outwards, i.e., from the inner bank of the upstream bend to the outer bank of the downstream bend. This further confirms that the combination of the dominant longitudinal transport and the cross-sectional motion determines the grains' distribution along the channel.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Bend**} & \multirow{2}{*}{**Section**} & \multicolumn{3}{c}{**Volume of**} & \multicolumn{3}{c}{**Proportions of D\({}_{1}\)–D\({}_{4}\) (\%)**} & \multirow{2}{*}{**D\({}_{4}\)**} \\  & & **(\(\times\)10\({}^{-4}\) m\({}^{3}\))** & & & & \\ \hline B\({}_{2}\), 30\({}^{\circ}\) flume & 13–21 (Left bank) & 1.44 & 20.5 & 66.1 & – & 13.4 \\ \hline B\({}_{2}\), 110\({}^{\circ}\) flume & 37–61 (Left bank) & 13.60 & 56.8 & 17.9 & – & 25.4 \\ \hline \hline \end{tabular}  
* For a sand bar around the convex bank (Bend B\({}_{2}\)), local grains initially located in the convex bank (D\({}_{3}\)) may be removed from the bend, while grains moved from the local concave bank and the upper bend should firstly offset the amount of grains being moved out.  
\end{table}
Table 4: Composition of point bars in the left bank of Bend B\({}_{2}\).