# Experiments on Longitudinal and Transverse Bedload Transport in Sine-Generated Meandering Channels
## 2 Experimental Setup and Measurements  
Experiments were conducted in the laboratory of the Institute of Geographic Sciences and Nature Resources Research, Chinese Academy of Sciences. The centerlines of the plexiglass meandering flumes under consideration follow the sine-generated curve with deflection angles (\(\theta_{0}\)) of 30\({}^{\circ}\) and 110\({}^{\circ}\), representing channels with small and large sinuosity, respectively (Figure 1). The two curved flumes share the same meander wavelength (\(\Lambda~{}=~{}2\pi~{}B\), where B is channel width), which is approximately 2.518 m, while their curve lengths are 2.694 m and 9.298 m, respectively. Table 1 summarizes the channel characteristics and the hydraulic conditions of the experimental runs. The curve lengths were calculated in curvilinear orthogonal coordinates, i.e., longitudinal (s) and transverse (n) (Figure 1). The upstream end of each curved flume was connected to a 0.8 m-long straight approach channel; the downstream end was connected to a 0.6 m-long straight exit channel. The banks are rigid. The flume widths are constant at 40 cm, and the cross sections are rectangular. The flumes were installed on a basin equipped with a water recirculating system. The flow was turbulent and subcritical based on the Re and Fr values (Table 1); tailgates were used to keep the initial water depths uniform along the channels. The water temperature was approximately 14 \({}^{\circ}\)C.  
The channel beds were paved with well-sorted silica sand with a specific density of 2.65 and a mean diameter \(\rm D_{m}=1\) mm. We chose relatively coarser grains to avoid sand waves on the beds as far as possible during bed deformation. The initial thicknesses of the sediment layer in the two experimental flumes were 5 cm and 8 cm, respectively. The run started from a bed with zero transverse slope. Specified longitudinal slopes, i.e., 1.12% and 2%, were set up for the \(\rm\theta_{0}=30^{\circ}\) and 110\({}^{\circ}\) flumes, respectively. Besides, the flow rates were designed as 60 and 50 \(\rm m^{3}/h\), respectively, for the two experimental runs. We chose these slopes and discharges to maintain moderate sediment transport rates in both experimental runs. Too much erosion would result in a scouring of the glass bottom, while too slow sediment transport rates would unnecessarily expand the experimental time and cost. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \(\theta_{0}\) & **Run** & \(\Lambda\)**(m)** & \(\Lambda\)**(m)** & \(\delta\) & \(\begin{array}{c}\mathbf{Q}\\ \mathbf{(m^{3}\;h^{-1})}\end{array}\) & \(\mathbf{B}\) & \(\begin{array}{c}\mathbf{hm}\\ \mathbf{(cm)}\end{array}\) & \(\mathbf{B/hm}\) & \(\mathbf{S}\) & \(\begin{array}{c}\mathbf{Um}\\ \mathbf{(m\;s^{-1})}\end{array}\) & \(\mathbf{Re}\) & \(\mathbf{Fr}\) \\ \hline \(30^{\circ}\) & \(30/1\) & 2 518 & 2.694 & 1.07 & 60 & 40 & 11.5 & 3.48 & 1.12 & 0.31 & 35,650 & 0.29 \\ \(110^{\circ}\) & \(110/1\) & 2 518 & 9.298 & 3.70 & 50 & 40 & 10.0 & 4.00 & 2.00 & 0.27 & 27,000 & 0.27 \\ \hline \end{tabular} Note: \(\theta_{0}\) is the deflection angle; \(\Lambda\) is the meander wavelength; \(\lambda\) is the length of a curved channel over one meandering wavelength; \(\delta\) is the sinusoid; \(\rm Q\) is the flow discharge; \(\rm D_{0}\) is the mean diameter; \(\rm B\) is the flow width; \(\rm{hm}\) is the channel-averaged flow depth; \(\rm S\) is the bed slope; \(\rm Um\) is the channel-averaged flow velocity; \(\rm Re\) is the flow Reynolds number; and \(\rm Fr\) is the Froude number.  
\end{table} 
Table 1: Flow and geometry characteristics of the two experiments. Figure 1: Experimental setup and the initial distribution of bed materials (unit: mm); inserts (**a**) and (**b**) are photos of the \(\rm\theta_{0}\) = \(30^{\circ}\) and \(110^{\circ}\) flumes, respectively. In order to obtain various fluvial regimes (will be discussed later), we designed a steeper slope for the \(\theta_{0}=110^{\circ}\) plume.