# Numerical Simulation of the Influence of Spur Dikes Spacing on Local Scour and Flow
## 1 Introduction  
Investigation of the local scour and flow field around spur dikes has a long history and remains a significant research focus area. The spacing between spur dikes is an important parameter for developing an appropriate relationship between multiple spur dikes in a group. [PERSON] et al. [1], [PERSON] et al. [2], and [PERSON] et al. [3] studied the scour processes around grouped spur dikes on the basis of aspect ratios, i.e., \(Ll\), where \(L\) is the length (distance) between two neighboring spur dikes, and \(l\) is the length of the spur dike. The maximum scour depth varies with the location of the spur dike under investigation. Usually, the maximum scour is found near the head of the first upstream spur dike, while the other scour depths vary due to the effect of neighboring spur dikes [4]. [PERSON] et al. [5] analyzed the scour problem of grouped spur dikes with spacing for \(3l\). Their study shows that the maximum scour depth of dikes along the groyne head is reduced, and the fourth spur dike scour depth can be ignored in a group of nine. [PERSON] et al. [6] found that the maximum scour depth is located at the first spur dike. For spur dike stability, a protection spur dike is positioned before the first one to reduce the impact of the scour on spur dike safety. Use of the flume test revealed that the distance between the cover and first spur dikes must be 1.5-2 times the groyne length. [PERSON] et al. [7] concluded that the maximum scour depth always develops on the upstream side of the first spur dike. After this experimental study, it was found that the first spur dike was more affected than the second, but this finding can only be applied up to \(4l\) spacing for the case of two spur dikes. When \(4l\) spacing is exceeded, both spur dikes experience approximately the same amount of scour under clear-water conditions. [PERSON] and [PERSON] [8] found that the scour depth and volume decrease with the increase of spur dike spacing when the spacing is less than \(4l\) for an impermeable spur dike. When thespacing is 4\(l\), the maximum scour depth decreases to 44% of the maximum scour depth for a single spur dike. Moreover, when the spur dike distance is 6\(l\), the maximum scour depth and erosion volume are larger than when it is 4\(l\). Considering the maximum scour depth and erosion volume, 4\(l\) is the most suitable distance for impermeable spur dike spacing. The existence of the spur dike changes the flow field characteristics of the original flow field, creating complex hydrodynamic characteristics such as flow separation, vortex shedding, and dive flow, so that the local flow presents strong three-dimensional characteristics. Obtaining accurate flow field information has always been a topic of concern for science and engineering. [PERSON] et al. [9], [PERSON] et al. [10], [PERSON] et al. [11], and [PERSON] et al. [12] studied the flow behavior around spur dikes. [PERSON] [13] studied mean flow and turbulence around a series of straight and angled spur dikes. Measurements showed that the turbulent intensities, Reynolds stresses, and turbulent kinetic energy increase considerably around spur dikes. The highest magnitude of bed shear stress and turbulent kinetic energy was consistently observed around the second spur dike in the series. [PERSON] [14] observed three-dimensional velocities of flow around spur dikes by Acoustic Doppler Velocimetry (ADV). The conclusion indicated that the initiation and development of local scour is determined by the turbulence intensity in the vertical direction rather than the bed shear stress. Higher shear stresses will transport more bed load, but not necessarily result in local scour. [PERSON] et al. [15] conducted an experimental study into flow velocity and shear stress. Considering the abutment protrusion ratios and flow conditions, they explained that the velocities near an abutment are magnified up to 1.5 times the approach flow velocity, and the shear stresses are enlarged up to 10 times the approach bed shear stress.