## 4 Partitioned Strong Coupling Formulation
[47] range from 200 to 1400; thus, further comparison between their predictions and the present numerical simulations seems erratic when \(Re>1400\). A perfect match between the present numerical simulations and the analytical predictions from [PERSON] and [PERSON] [19] has been achieved, except for \(Re=1500\). This implies that the present numerical model predicts the drag coefficient of a flexible net panel reasonably well when \(Re<1500\). Figure 4: Dependence of the drag coefficients of the flexible net panels on the Reynolds number [19; 47]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(Re\) & \multicolumn{6}{c}{**Drag Coefficient/Relative Difference**} \\ \hline  & **Num. ** & **Num. ** & **[PERSON] et al. [47]** & **[PERSON] and [PERSON] [19]** \\ \hline  & \(Sn=0.16\) & \(Sn=0.33\) & \(Sn=0.16\) & \(Sn=0.33\) & \(Sn=0.16\) & \(Sn=0.33\) \\
300 & 0.221 & 0.747 & 0.184 & 0.686 & 0.250 & 0.719 \\  & & &



## 6 Results and Discussion

### Velocity Distribution

The wake forms behind the net panel when the flow passes through it. Figures 5 and 6 depict the velocity distributions of two flexible net panels at different velocities. We see that the width of the wake is nearly the same as that of the net panel when the flow velocity is small. The width of the wake in the far field diminishes gradually as the flow velocity increases. This is mainly because the reconfiguration of the net causes a change in the pressure gradient, leading to the far-field wake diminishment. There is a slight velocity reduction upstream of the net panel; the velocity reduction in the downstream far-field region is relatively large compared to the upstream velocity reduction. The flow velocity reaches the steady state in the far-field region. However, the velocity accelerates dramatically in the near-field region where the wake flow does not block flow the net. Figure 5: Velocity distributions of the flow at the angles of attack between \(\pi/3\) and \(\pi/2\) for net solidities \(Sn=0.16\) (**left** column) and \(Sn=0.33\) (**right** column): (**a,b**) \(U_{\infty}=0.15\) m/s; (**c,d**) \(U_{\infty}=0.30\) m/s; (**e,f**) \(U_{\infty}=0.45\) m/s. Figures 5 and 6 present distinct flow patterns where the velocity reduction increases alongside the net solidity, meaning that higher solidity can cause a greater shielding effect in the flow field. As the net solidity reaches 0.33, we see clear interference between net twines. This interference causes energy losses when the flow passes the net twines and further affects the flow transition. Consequently, higher solidity results in greater velocity reduction. There is no such interference between net twines when \(Sn=0.16\). The velocity reduction is relatively large if the free stream flow velocity is small; this could be attributed to the large drag coefficient at a lower Reynolds number [48]. The velocity reduction becomes smaller as the inclination angle of the net increases. The inclination angle of the net is denoted as \(\pi/2-\alpha\), where \(\alpha\) is the angle of attack. In other words, the velocity reduction decreases as the attack angle decreases. This is consistent with the numerical studies in [PERSON] et al. [13,14]. Moreover, a large inclination angle produces a distinct velocity gradient that could cause severe fluctuations regarding velocity reduction. It appears that the flow characteristics of the nets may not only depend on the solidity ratio and the angle of attack but also on the flow regime (i.e., \(Re\)). Hence, two flow regimes are identified in this paper according to [PERSON] [49]:

1. Transition-in-wake state of flow (\(\mathbf{TrW}\)). 2. Transition-in-shear-layers state of flow (\(\mathbf{TrSL}\)). In the \(\mathbf{TrW}\) state, the laminar periodic wake becomes unsteady at a higher Reynolds number further downstream. The transition spreads from upstream alongside the Reynolds number, until the eddy becomes turbulent during its formation.