## 1 Introduction  
The majority of bridge failure incidents are caused by the scour phenomenon at bridge pier foundations. The level and the type of bridge pier foundations are directly related to the scour depth that has a significant impact on the bridge's construction cost. A better understanding of the flow structure and the bed shear stress distribution around bridge piers will enhance the prediction of the scour depth, and consequently will reduce the bridge construction cost. In numerical modeling simulations of the flow structure around piers, no agreement among researchers has been achieved regarding the appropriate turbulence model for the numerical simulation. Additionally, most of the previous flow structure numerical simulations have been carried out using rigid flat bed and/or solidified equilibrium scoured bed geometries. Numerous laboratory studies have been carried out to develop equations to predict the maximum scour depth [1; 2; 3; 4; 5; 6; 7; 8; 9]. The available experimentally developed scour equations have been investigated and were found to over predict the scour depth, especially for skewed, long, and wide piers [10]. In subcritical flow conditions where the Froude number \(<1\), the maximum ratio between the equilibrium scour depth and the pier diameter (\(d_{se}/D\)) was experimentally obtained around 2.4 [11]. Other experiments under supercritical flow conditions revealed that (\(d_{se}/D\)) reached 3.0 at a Froude number = 1.5 [4]. The development of local scour at bridge piers is directly affected by the flow field structure around the pier and near the bed where downward flow, \(HV\), and wake vortices are generated. The stream velocity decelerates while approaching the pier until it reaches stagnation at the pier's upstream side face. The generated stagnation pressure gradient between the water surface and the bed at the pier's upstream face generates a downward flow [12]. The generated downward flow acts as a vertical jet, which plays a significant role in the erosion of the bed material and the formation of the scour hole [13]. It has been claimed that the \(HV\) is a consequence of scouring, not the cause of it [12]. Therefore, a better understanding of the dynamic interaction between the flow field and the scouring process is still a pressing need to accurately simulate and predict the scour depth. Several researchers have conducted experimental investigations of the flow field structure through the development of scour holes around piers [14; 15; 16; 17; 18; 19; 20; 21]. The scour hole is initiated by two small scour holes at \(\pm 100^{\circ}\) to the flow direction. They then move around the pier perimeter and merge at the pier's upstream side along the stream centerline [14]. The maximum magnitude of the downward velocity (\(V\)) in front of the pier has a wide range of reported values relative to the depth-averaged approach velocity (\(U_{o}\)). The values varied between (\(-0.47\)\(U_{o}\)) [18], (\(-0.60\)\(U_{o}\)) [16; 17; 19], (\(-0.80\)\(U_{o}\)) [14], and (\(-0.95\)\(U_{o}\)) [15]. The development of \(CFD\) models motivated the use of numerical simulations [22; 23; 24; 25; 26]. No agreement among researchers has been achieved regarding the appropriate turbulence model for the numerical simulation of the flow structures and the bed shear stress around the bridge piers. The (\(k\)-\(\epsilon\)) model was recommended by the authors of [27; 28; 29], while the (\(k\)-\(\omega\)) was recommended by the authors of [30; 31], and the Reynolds Stress Model (\(RSM\)) was found to provide satisfactory results [32]. The (\(k\)-\(\epsilon\)) and the (\(RNG\)\(k\)-\(\epsilon\)) turbulence models provide identical results for bed shear stress [33]. The increase in computational and digital storage capacities has led to an increase in \(LES\) and \(DES\) models. \(LES\) and \(DES\) have proved adequate in simulating large scale coherent eddies around piers [34; 35].