# Numerical Study of the Flow and Blockage Ratio of Cylindrical Pier Local Scour
## 5 Conclusions  
Despite important research efforts over the last decade, there are still difficulties in accurately predict the maximum value of \(S/D\) ([PERSON] et al., 2023 [50]). It is for this reason that a correct understanding of the kinematics of the scour at the base of an obstacle are vital for designing and constructing sustainable hydraulic structures. This study presents a numerical model using the LES approach. The code was initially developed by [PERSON] et al., 2020 [20] for a wide channel in live-bed conditions in the turbulent rough regime (\(\text{Re}_{D}\approx 46\),000). In the present study, we successfully studied the combined effect of the velocity and the blockage with a focus on an approaching flow near the hydraulically smooth regime. We consider two different test cases. The first case presents a good agreement with the experimental findings of [PERSON] et al., 2005 [4] (\(\text{Re}_{D}\approx 46\),000), with the objective of acting as a control case to ensure that the model could still accurately predict the scouring process in the live-bed regime after the extension of the applicability to the clear-water regime and the generalization of the flow conditions. A moderately low  
Figure 17: Scour depth evolution upstream of the cylinder for the clear-water (CW) and live-bed (LB) cases. Reynolds number (Re\({}_{D}\approx 2000\)) is used for the second case to study the model's ability to predict clear-water scour. Validation is achieved by qualitatively and quantitatively comparing the predicted scour depth and time evolution with a laboratory experiment reported in Lachaussee, 2018 [18]. We obtain fair agreement with the velocity profile obtained using PIV measurements in the narrow channel with non-slip lateral wall boundary conditions. Although the numerical model still has discrepancies at the lee-side of the dune and downstream of it, the accuracy of the predicted angle, size, and depth of the scour hole are very good near the obstacle. This is despite the difference in the height of the cylinder and despite the fact that the experimental set-up uses a submerged cylinder while the cylinder in the numerical set-up is only partially submerged. This behavior is consistent with the conclusion regarding the height-diameter ratio of the obstacle in Lachaussee, 2018 [18]. The model can also accurately predict the depth evolution of the scour hole. However, in the long-term simulation, the model reaches its equilibrium at a greater depth. This behavior could be a consequence of the sediment bed hypothesis as a continuum, the pier \"shadow effect\" on the measurement technique, or a combination of both. The amplification to the flow contraction caused by the confinement is well described by the model. In the clear-water case, the narrow channel simulation presented a higher scour depth than the wide channel simulation. These results show that a large blockage ratio (\(D/W\geq 0.1\)) can have an important impact over the scour process, despite a low relative coarseness (\(D/d<100\)). However, because all tests in the present study were performed for low Froude number values, it would be interesting to perform a similar study for a higher value Froude number to account for the free surface effects on the scouring process. Future study will focus on testing similar flow conditions with different pier geometries. M.H.-H.: Methodology, Writing, Validation; W.Z. : Methodology, Conceptualization; A.H.: Methodology, Writing; D.P.V.B. : Project administration, Methodology, Conceptualization, Supervision; K.D.N. : Methodology, Conceptualization. All authors have read and agreed to the published version of the manuscript. This research was partially funded by the Quebec Ministry of Foreign Affairs (MRIF, project AVOCAP-2021-2023) and the Mexican Council of Science and Technology (Investigadoras e Investigadoras e Investigadoras for Mexico, CONACYT).