## 2 Experimental Setup and Methods
### Measurement Parameters  
#### 2.3.1. Bedform Parameters  
The bedforms generated in this experiment exhibit both 2D and 3D topographies. In this study, three longitudinal profiles were extracted: one from the center of the flume width and two others at intervals of 20 cm to the left and right. Additionally, cross-sectional profiles were extracted every 3 m along the length of the flume, starting from the 2 m position, as shown in Figure 4. From the longitudinal profile perspective, the arrangement of crests and troughs on the 2D bedform is noticeably more regular than that on the 3D bedform (Figure 4a,c). From the cross-sectional profile perspective, the elevation variation across the flume width is significantly smaller for the 2D bedform compared to that for the 3D bedform (Figure 4b,d).  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**J**} & \multirow{2}{*}{**No.**} & \(Q\) & \(\boldsymbol{h}\) & \(\boldsymbol{u}\) & \(\boldsymbol{Fr}\) & \(\boldsymbol{Re}\) & \(\boldsymbol{u^{\star}}\) & \(\boldsymbol{g_{b}}\) \\  & & **1/s** & **cm** & **m/s** & \(\times\)10\({}^{4}\) & **cm/s** &  
To analyze the evolution of bedform features, four longitudinal profiles of bed elevation were extracted at 20 cm intervals across the flume width (excluding the boundaries) from left to right for each experiment.  
In this study, the 2D and 3D dune bedforms were analyzed after detrending using the original bed height as the zero axis at equilibrium. Subsequent to each experiment, the length, height, crest height, and trough depth of the dunes were examined. The relative positions of these bedform parameters are illustrated in Figure 5.  
(1) Dune length  
This research defines four types of dune lengths: _Lc_, the horizontal distance between the adjacent crests; _Lt_, the horizontal distance between the adjacent troughs; _L_upcr, the horizontal distance between two adjacent nodes with positive slopes on the zero axis at equilibrium; and _L_downcr, the horizontal distance between two adjacent nodes with negative slopes on the zero axis at equilibrium. The average lengths for each type are denoted as _Lc-ave_, _Lt-ave_, _Lupcr-ave_, and _Ldowncr-ave_, respectively. The \"average\" value for each bedform parameter was calculated as the arithmetic mean of the corresponding values obtained from the identified bedforms.  
(2) Dune height  
Dune heights are typically categorized into two types: the stoss-side dune height (\(\Delta s\)), which is the vertical distance between the crest and the adjacent upstream trough, and the lee-side dune height (\(\Delta l\)), which is the vertical distance between the crest and the  
Figure 4: Schematic diagram of the longitudinal and cross-sectional features of the 2D and 3D bedforms. (**a,b**) represents the longitudinal and cross-sectional profiles of the 2D bedform, respectively, while (**c,d**) represents the longitudinal and cross-sectional profiles of the 3D bedform.  
adjacent downstream trough. The average stoss-side and lee-side dune heights are denoted as \(\Delta s\)-_ave_ and \(\Delta l\)-_ave_, respectively.  
(3) Crest height and trough depth  
In this study, the crest height (\(\eta c\)) is defined as the vertical distance from the crest to the zero axis at equilibrium, whereas the trough depth (\(\eta t\)) represents the vertical distance from the trough to the zero axis at equilibrium. The average values for the crest height and the trough depth are represented as \(\eta c\)-_ave_ and \(\eta t\)-_ave_, respectively.