Experimental Study of Flow in Prismatic Compound Channel with Inclined Floodplains

Introduction
A compound channel usually consists of a main channel in the middle and one or two floodplains around it. The flow velocity in the main channel is higher than the floodplains, due to its greater depth and smaller roughness. This difference causes the formation of a shear layer at the interface between the main channel and floodplains (as shown by Sellin, 1964); Shiono and Knight, 1991; Tominaga and Nezu, 1991; Bousmar, 2002; and Rezaei, 2006). Tominaga and Nezu (1991), Rezaei (2006), and Sum (2007) investigated the velocity distribution in prismatic compound channels. Their observations showed that the highest flow velocity is below the free surface. In prismatic compound channels, as the relative depth increases, the difference between the velocity in the main channel and floodplains decreases. At high relative depths, the effect of the shear layer formed between the main channel and floodplains can be almost ignored (Knight et al., 2018). The maximum interactions between the main channel and floodplains have been observed in relative depths between 0.1 and 0.3 (Shiono and Knight, 1991; Rezaei, 2006). Investigations reviled that, so far, the effect of the floodplain's side slope in prismatic compound channels has not been investigated. The main objective of this research is the experimental study of the flow field in the prismatic compound channel with inclined floodplains.
Methodology
This research was carried out on the flume located in the hydraulic research laboratory of Bu-Ali Sina University. The flume is 18 meters long, 1.2 meters wide, and 0.6 meters deep with a bed slope of 1.63×10-3. Figure 1 shows an overview of the research channel used in this research. In this flume, smooth and rigid boundaries were constructed using PVC material. As seen in Figure 2(b), the flume has a compound cross-section with a 0.4 m main channel wide, 0.05 m deep, and also two 0.4 m wide inclined floodplains (lateral slope of 0.075). The downstream end of the flume has an adjustable tailgate which is used to control the water surface profile and make uniform flow along the flume. In all experiments, the water surface profiles were measured using a pointer gauge with an accuracy of 0.1 mm. Velocity distributions were measured using an Acoustic Doppler Velocimeter (ADV) every 20 mm laterally and every 10 mm vertically (see Figure 3). The lateral distributions of boundary shear stress were also measured using a Preston tube (outer diameter 4 mm). The velocity distributions and boundary shear stress were measured for five discharges of 27, 30, 35, 40, and 45 lit/s.
Results and Discussion
The velocity distributions for different discharges are shown in Figure 4. From the figure, it is clear that in the vicinity of the junction edge, the isovel lines bulge upward, and the velocity is decelerated, probably due to low mass and momentum exchanges in this region. Near the main channel walls (0.1 m < y < 0.18 m), the isovel lines bulge downward, and the velocity is accelerated. Also, near the middle of the main channel (0 < y < 0.1 m), the isovel lines bulge upward, and flow is decelerated due to flowing away from the main channel bed.
As seen in Figure 3, the flume cross-sectional area was divided into subareas. The point velocity distributions were integrated numerically over the local water depth at each subarea to get the streamwise depth-averaged velocity. The results of depth-averaged velocity calculations for different relative depths are shown in Figure 5. In order to investigate the effect of the floodplain's side slope on the velocity distribution, the depth-averaged velocity has been normalized (Ud/Um) and compared to Rezaei’s Data (see Figure 7). The normalized depth-averaged velocities in the main channel, are almost equal to Rezaei’s data (with some fluctuations). While on the floodplains, those velocities are less than Rezaei’s Data (velocity in compound channels with flat floodplains).
Boundary shear stress is used in river engineering and in studies related to riverbed protection and sediment transport. The boundary shear stress distributions for different discharges are measured and shown in Figure 8. As seen in Figure 8, the bed shear stress distribution follows the same pattern as the depth-averaged velocity.
The apparent shear forces at the vertical interface between the main channel and floodplains can be calculated using the momentum equation for a control volume in the main channel (see Figure 12). The results of the apparent shear force calculation show that by increasing discharge or relative depth, the apparent shear force increases and reaches its peak value at a relative depth of 0.363 (see Table 3). The apparent shear forces expressed as a percentage of the total channel shear force on the vertical interface are shown in Figure 13. From Figure 13, it can be seen that the percentage of apparent shear forces at the interface between the main channel and floodplains are always smaller than those values in the compound channel with flat floodplains.
Conclusion
In this research, the flow field, including the velocity and bed shear stress distribution, in a prismatic compound channel with inclined floodplains (side slope 0.075) has been studied, experimentally. The results of experiments have been also compared with Rezaei’s data. The most important results obtained from this research are as follows:
The depth-averaged velocity and boundary sear stress distributions follow the same pattern. Both of them show almost uniform flow in the main channel with some fluctuations. While in the flood plains, they are non-uniform with an extreme decreasing trend. In the main channel, the normalized depth-averaged velocity and normalized boundary shear stress are almost similar to Rezaei’s Data. While on floodplains, the normalized velocity and shear stress are non-uniform and less than Rezaei’ data. The study also shows that the apparent shear force at the interface between the main channel and floodplains increases with the increasing relative depth and reaches a peak value at the relative depth of 0.3. The same observations were made by Shiono and Knight (1991), and Rezaei (2006).