# Numerical Simulation of the Influence of Spur Dikes Spacing on Local Scour and Flow
## 6 Conclusions  
In this paper, a sedimentation scour model was presented to simulate the variation of the local bed configuration around grouped spur disks. The model calculated all aspects of the sediment transport process, including bed-load transport, entrainment, deposition, and suspended load transport for each species, using a stochastic approach. By applying the model to simulate sediment transport around grouped spur disks in an experimental flume, it was found that the maximum scour depth formed in the vicinity of the first spur dike head. With the increase in spur dike spacing, the shielding effect of  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Scour Depth/Shear Stress** & \multicolumn{3}{c}{**Correlations**} \\ \cline{2-4}  & \(2l\) & \(3l\) & \(4l\) \\ \hline Pearson Correlation & 0.789 & 0.863 & 0.968 \\ Sig. (2-tailed) & 0 & 0 & 0 \\ N & 25 & 25 & 25 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The scour depth and shear stress correlations.  
Figure 10: The relationship curve of scour depth and shear stress. (**a**) for \(2l\) spacing; (**b**) for \(3l\) spacing; (**c**) for \(4l\) spacing.  
the first spur dike was weakened. On the whole, the numerical simulations reproduce quite well the experimental outcomes under a qualitative point of view.  
The maximum velocity, which was twice the approach flow velocity, appeared in the main flow area between spur dike I and spur dike II in the fixed bed. The maximum flow velocity in the main flow zone in the final configuration essentially matched the incoming velocity. The streamline around spur dikes was obviously three-dimensional and was mainly characterized by the horizontal separation flow and the vertical downward flow. The area with the maximum turbulent energy appeared at the junction of the high-velocity main flow area and the backflow area between spur dikes, especially in the backflow area of spur dike IV in the fixed bed. In contrast, in the movable bed, the maximum value appeared at the head of spur dike II. The maximum shear stress appeared in the main flow zone between spur dikes I and II on the fixed bed and was up to 10 times the approach shear stress. With the development of scouring, the shear stress decreased. The analytic results correlate significantly, which indicates that bed shear stress plays a leading role in the scouring process.  
Given the above results, there is a high potential for the understanding and subsequent variation of spur dike spacing to be put to practical use in real rivers. However, further refinement to the sedimentation scour model is necessary to account for non-uniform sediment. Moreover, fundamental experiments and numerical simulation are also needed to investigate realistic irregular border channels and hydraulic structures such as grouped spur dikes of unequal length and unequal spacing.  
[PERSON], [PERSON] and [PERSON] conceived and designed the framework of this study, analyzed and discussed the results, and wrote the paper. [PERSON] treated the test data and performed the model simulation.  
This research was funded by Science and Technology Projects of the Shaanxi Water Conservancy Department [grant number 2017/slkj-17], and Key R&D Program Projects in Shaanxi Province [grant number 2018 SF-352], the National Natural Science Foundation-sponsored project [grant number 51579206], Xi'an University of Technology Doctoral Innovation Fund [grant number 310-252071507].  
The authors declare no conflict of interest.