# Development of a Two-Dimensional Hybrid Sediment-Transport Model
## 4 Examples and Application
### East Fork River  
The East Fork River is a typical meandering river located in Wyoming State that was used for the study of bed-load transport in the 1970s. The selected reach was about 3.3 km long with the channel width varying from 16 m to 45 m and ending at a bed-load trap across the river (Figure 6). The flow in this river was influenced by spring runoff due to snowmelt, with rising flow rates in the morning, peak rates at midday, and declining flows in the afternoon. This field case was selected to demonstrate the capability of the model for long-term sediment transport under unsteady turbulent-flow conditions.  
Figure 5: Longitudinal bed profiles at different times.  
Figure 6: Selected reach of East Fork River. Solid circles represent the approximate locations of bed samples.  
The simulation period was 2-19 June 1979. Figure 7 shows the hydrograph and the stage graph at the inlet and outlet. This model generated an unstructured quadrilateral mesh of this reach with minimum and maximum edge lengths equal to 0.46 m and 13.99 m (Figure 8). With the variation of flow, the wetting-and-drying process developed with time in this study reach, which may have induced nonphysical numerical oscillations in the model. The multipoint momentum interpolation correction technique [51] was used to remove the oscillations and maintain numerical stability and accuracy.  
The measured water surface elevation at section 107 was used to calibrate the Manning coefficient, and Figure 9 compares the simulated and measured water surface profiles at section 107 using the calibrated Manning coefficient of 0.03 m\({}^{-1/3}\)s for the whole reach and the time step of 3 s. As can be seen, the simulated profile matched well with the measured one.  
Figure 8: Local view of unstructured quadrilateral mesh with 16,533 cells and 16,000 nodes.  
Figure 7: Hydrograph at the inlet and stage graph at the outlet.  
Table 3 lists the initial nine size classes of sediment mixtures ranging from 0.088 mm (fine sand) to 32 mm (coarse gravel). Bed-sample information was obtained from the USGS technical report [52] for the selected reach. Although the bed load was dominant, both the suspended-load and bed-load transport were simulated. In this simulation, the adaptation coefficient of the suspended load, \(\alpha\), was calibrated as 0.001, while the adaptation length of the bedload, \(L_{b}\), was 60 m, about two times the average channel width.  
At the outlet, the measured sediment flux at the bed trap was available to compare with the simulated one (Figure 10). According to the comparisons, the sediment-transport model captured the general trend of the variation of the sediment discharge with time, except for the overestimation of the first peak and the underestimation of the second peak. The simulation results were also identical to the ones from [PERSON] [19].  
Figure 10: Sediment discharge at the outlet.  
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Size (mm)** & **0.088** & **0.177** & **0.354** & **0.707** & **1.41** & **2.83** & **5.66** & **11.3** & **32** \\ \hline Fraction & 0.044 & 0.00038 & 0.02 & 0.478 & 0.233 & 0.145 & 0.093 & 0.02 & 0.01 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Sediment size classes for the East Fork River ([PERSON] et al. [52]).  
Figure 9: Water surface profiles with time at section 107.