Experimental Study of the Effect of the Dune Bed Form Height on Manning's Roughness Coefficient

Manning's equation is the most popular equation to determine the flow resistance in the steady and uniform flows. The amount of flow resistance in alluvial rivers depends on the type of bed form and its geometrical characteristics. In ripple and dune bed forms, which are formed at Froude numbers less than one (lower flow regime), the flow separation from their crest is the main factor of flow resistance (Shafai Bajestan, 2008; Julien, 2010). The effect of bed form on flow resistance have been studied by few researchers such as: Talebbeydokhti et al. (2006), Omid et al. (2010), Nasiri Dehsorkhi et al. (2011), Chegini and Pender (2012), Kabiri et al. (2014), Samadi-Boroujeni et al. (2014), Kwoll et al. (2016), and Heydari (2020). However, no research has been observed regarding the effect of the dune bed form height on Manning's roughness coefficient. Therefore, the main goal of the present study is to investigate the effect of dunes with different height of 1, 2, 3, and 4 cm on Manning's roughness coefficient in a straight flume under different discharges and bed slopes.

The experiments were performed in a straight flume of 12 m in length and 0.30 m wide (Figure 1). In this study, different flow discharge of 10, 15, 20, 25, and 30 l/s and different bed slopes of 0.00001, 0.0001, 0.0005, 0.001, and 0.0015 were tested. Each dune was made in an asymmetric triangular shape with cement-sand mortar. The dune's height was equal to 1, 2, 3, and 4 cm, and the its length was selected as 25 cm. After each dune was built, the sediment with average size (d50) of 0.45 mm was glued to its surface. The total number of experiments in the present study was 100. Dune bed form dimensions were in lower flow regime. All the experiments were carried out at lower flow regime with, the Froude number values ranged from 0.44 to 0.7.

Figure 4 shows the variation of the Manning's roughness coefficient against relative submergence (y/Δ) for dunes with a height of 1 cm. This figure shows that, with increasing relative submergence and bed slope, Manning's roughness coefficient decreased.Figure 5 shows the changes in the Manning's roughness coefficient against Froude number for dunes with different heights (slope of 0.0001). It can be seen that as the Froude number increased, the Manning's roughness coefficient decreased.
Figure 7 illustrates the effect of Δ/λ on the Manning's roughness coefficient. This figure shows that the Manning's roughness coefficient increased with increasing Δ/λ. Calculations showed that the Manning's roughness coefficient in dunes with Δ/λ = 0.08, 0.12, and 0.16 was, on average, 17, 30, and 55% more than dune with Δ/λ = 0.04, respectively.Figure 8 shows the effect of the dune bed form height on the Manning's roughness coefficient. By increasing bed form height, Manning's roughness coefficient increased. Calculations showed that the Manning's roughness coefficient in dunes with height of 2, 3, and 4 cm was, on average, 16, 31, and 55% more than dune with a height of 1 cm, respectively.

The results of this study shows that with increasing the Froude number and the relative submergence (y/Δ), the flow resistance or Manning's roughness coefficient decreases. Moreover, the increase in the Δ/λ and the bed form height leads to an increase in Manning's roughness coefficient. Calculations showed that the Manning's roughness coefficient in dunes with height of 2, 3, and 4 cm was, on average, 16, 31, and 55% more than dune with a height of 1 cm, respectively. In addition, the form Manning's roughness coefficient (nb'') for dunes with heights of 1, 2, 3, and 4 cm is, on average, 30.7, 40.2, 46. 5, and 53.4% of the total Manning's roughness coefficient (nb), respectively.