## 2 Materials and Methods
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Run Number** & **Total Domain Cells** & **Fluid Sub Domain Cells** & **Solid Sub Domain Cells** & **Partially Wet Cells** \\ \hline
1-(\(ds/des=0.00\%\)) & 13,764,080 & 8,870,812 & 179,306 & 4,713,962 \\ \hline
2-(\(ds/des=30.0\%\)) & 13,764,080 & 8,874,962 & 180,935 & 4,708,183 \\ \hline
3-(\(ds/des=47.0\%\)) & 13,764,080 & 8,888,140 & 184,195 & 4,691,745 \\ \hline
4-(\(ds/des=69.0\%\)) & 13,764,080 & 8,903,531 & 187,177 & 4,673,372 \\ \hline
5-(\(ds/des=78.0\%\)) & 13,764,080 & 8,910,260 & 187,515 & 4,666,305 \\ \hline
6-(\(ds/des=92.0\%\)) & 13,764,080 & 8,922,547 & 188,995 & 4,652,538 \\ \hline
7-(\(ds/des=100.0\%\)) & 13,764,080 & 8,940,817 & 191,613 & 4,631,650 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Variation of the domain cell numbers for the current study simulations. Figure 3: Coordinate system. The turbulence phenomenon is characterized by its spatial and temporal rapid changes in the flow field. To capture the turbulence by applying mass and momentum conservation equations, the use of a very small grid resolution with a very small-time step is required. The available computational and storage resources have not been sufficient until now to conduct such a fine-scale simulation [44]. Turbulence simplified models can simulate the turbulence effect on flow parameters. Recently, _LES_ turbulence modeling has gained increasing attention, and was used for the first time to investigate the flow field and the scouring potential around piers in 2013 [47]. The LES requires vast computational and storage resources, which are not readily available for personal computer-based _CFD_ simulations. The Reynolds Averaged Navier Stokes (_RANS_) turbulence models provide an inexpensive solution for the _CFD_ simulation of the turbulence effect on flow parameters. No agreement among the researchers has been achieved in the literature for the most suitable turbulence model to be used in similar cases to the current study. The Renormalization Group _RNG_\(k\)-\(\epsilon\) turbulence model was recommended by the authors of [32; 27; 28], and the \(k\)-\(\omega\) turbulence model was recommended by the authors of [27; 28; 29], and the \(k\)-\(\omega\) turbulence model was recommended by the authors of [30; 31]. The three turbulence models RNG \(k\)-\(\epsilon\), \(k\)-\(\epsilon\), and \(k\)-\(\omega\) are evaluated in the current study. All turbulence models reached steady-state conditions upstream from the pier at relatively small simulation times. At the downstream side, a longer simulation time for the \(k\)-\(\epsilon\) and _RNG_\(k\)-\(\epsilon\) turbulence models was required, and no steady-state conditions were achieved for the \(k\)-\(\omega\) turbulence model. The numerical model simulated velocities \(u\) and \(v\) in their normalized form and \(u\)/\(U_{o}\) and \(v\)/\(U_{o}\) were validated against the experimental measurements obtained from [30] as shown in Figures 6 and 7. The results obtained from the three turbulence models were almost identical at the upstream side of the pier. At the pier's downstream side, the \(k\)-\(\epsilon\) and _RNG_\(k\)-\(\epsilon\) turbulence models reached steady state conditions, which is not the case in reality due to the existence of vortices and oscillations at the downstream side. The \(k\)-\(\omega\) turbulence model did not reach  
Figure 5: Variation of water depth and longitudinal and lateral velocities at point A for different mesh sizes. steady state conditions at the pier's downstream side and considerable flow oscillations were obtained. Figure 8 shows the resulting longitudinal velocity oscillation at the pier's downstream side for 10 s with a 0.5 s interval. The average values of the velocities in both the longitudinal and vertical directions show a non-uniform pattern close to the measured values near the pier as in the experimental results given in Figures 6 and 7.