# Modelling Regime Changes of Dunes to Upper-Stage Plane Bed in Flumes and in Rivers
## 6 Results with River Conditions
### Results for the More Extreme River Scenario  
With the artificial more extreme scenario, which includes an increase of the discharge of 5%, a transition to upper-stage plane bed is predicted. It should be noted that this transition was not observed in the river Waal in 1998 [PERSON] et al. (2002), nor in the Dutch Rhine Branches in 1995 when the discharge at Lobith was 25% higher than it was in 1998 (e.g., [PERSON] et al. (2002)). The computed development of the dune field, starting from an already developed dune field, can be observed in Figure 17.  
Here the growth and washing out of the dunes can be observed on the left, and the washing out itself can be observed more clearly on the right. From the same results, the development of the dune trough and crest positions (in the vertical) and water depth over time are shown below (Figure 18). As can be seen in the beginning of the run, dunes start developing along with increasing discharge. At around 137 h from the start of the model run, the dunes start washing out, and they're completely gone at about 141 h, 5 h before the maximum discharge occurs. Due to the decrease in form drag and thereby _total shear stress_, the water level goes down, despite still-rising discharge. The bed remains washed out until the discharge is low enough for dunes to start developing again. For the flood of 1998, dune heights in the Waal varied between 0.2 and 0.6 m on the centreline, while the model results indicate values between 0.2 and 2.2 m. In Figure 19 the response of dune height to changing discharge can be seen. The hysteresis loop observed here is in the opposite direction of the measured flood wave of 1998 as reported by [PERSON] et al. (2002) [PERSON] et al. (2002). Due to the washing out of dunes during the flood wave, dunes are now generally lower in the falling limb than in the rising limb. The relation between \(\alpha\) and the specific discharge for the rising and falling stages of the hydrograph can be seen in Figure 20.  
Figure 16: Specific discharge versus water depth separated for the rising and falling stages of the hydrograph, using the river scenario. The arrow signifies the direction of development over time. Figure 17: Dune field over time, using the more extreme river scenario. The right part zooms in on the dune field in the period where the transition occurs. Figure 18: Dune crest and trough position (black lines) and water depth (blue line) over time, using the more extreme river scenario. Here again a hysteresis effect is observed, caused by the transition to upper-stage plane bed and back to the dune regime. It should also be noted that now, much higher step lengths are reached, up until \(\alpha\) = 10,800, which is a dimensional step length of about 13 m. This is about 10 times the value of the plume scenario. For the river scenario of Section 6.1, the maximum step length was only 2.6 times higher than the plume scenario. This difference between the river scenarios mostly relates to the washing out of dunes, which only occurs for the more extreme river scenario. When the dune is washed out, water depth drops somewhat, but due to the lack of bedforms, the flow can exert more  
Figure 19: Discharge versus dune height for the rising and falling stages of the hydrograph, using the more extreme river scenario. The arrow signifies the direction of development over time. Figure 20: Specific discharge versus non-dimensional step length \(\alpha\) separated for the rising and falling stages of the hydrograph, using the more extreme river scenario. The arrow signifies the direction of development over time. force on the particles, which increases step length because that is partly based on grain shear stress. The effect of hysteresis on water depth can be seen in Figure 21.  
In the rising part of the hydrograph dunes are able to develop firstly at lower discharges, while in the falling part the dunes start developing at higher discharges. This has a clear effect on the resulting water depths at the same discharge.