## 4 Partitioned Strong Coupling Formulation
The overall trends of the non-dimensional recirculation width (\(W_{r}^{*}\)) are divided into two regimes, namely \(\textbf{TrW_{2}}\) and \(\textbf{TrS}\textbf{L_{1}}\). For \(Sn=0.16\) in the \(\textbf{TrW_{2}}\) regime, \(W_{r}^{*}\) increases alongside the Reynolds number, and a value around 1.57 is attained in the regimes where flow transfers from \(\textbf{TrW_{2}}\) to \(\textbf{TrS}\textbf{L_{1}}\). \(W_{r}^{*}\) drops in the \(\textbf{TrS}\textbf{L_{1}}\) regime where the minimum value is 0.83. However, in the post \(\textbf{TrS}\textbf{L_{1}}\) regime, \(W_{r}^{*}\) rises progressively to a maximum of 1.71 on the top section. This is mainly because the shear layers have been disturbed. For \(Sn=0.33\) in the \(\textbf{TrW_{2}}\) regime, the value of \(W_{r}^{*}\) decreases in the middle and bottom sections. However, it increases in the top section from the \(\textbf{TrW_{2}}\) to the \(\textbf{TrS}\textbf{L_{1}}\) regime and its value, in general, is smaller than those in the middle and bottom sections. The minimum \(W_{r}^{*}\), approximately 0.88, is obtained at \(Re=300\). Additionally, in the middle and bottom sections, \(W_{r}^{*}\) grows rapidly during the transition from the \(\textbf{TrW_{2}}\) to the \(\textbf{TrS}\textbf{L_{1}}\) regime and it reaches a peak value of 1.6. Then, \(W_{r}^{*}\) falls in the post \(\textbf{TrS}\textbf{L_{1}}\) regime. The net panels could be considered as a combination of cylinders (i.e., net twines). It is well known that \(W_{r}^{*}\) is related to the fluid force acting on a bluff body such as a cylinder, and that larger \(W_{r}^{*}\) causes a lower pressure area behind the body. Moreover, the reverse flow in the wake of the body influences the streamwise vortices. According to [PERSON] [49], larger \(W_{r}^{*}\) can lead to a higher \(C_{D}\) for circular cylinders. However, the net panel's flow characteristics are much more complicated than that of a system of cylinders. From this point of view, it may be helpful to compare the present simulation and the results from [PERSON] and [PERSON] [52], to facilitate a better understanding of how recirculation/vorticity behind net twines impacts flow characteristics of the net panel. Still, to provide more insights into the flow characteristics, studies on three-dimensional vortices of the net panel need to be conducted. This paper uses the Q-criterion [53] to identify the iso-surfaces of the three-dimensional instantaneous vorticities. By decomposing the velocity gradient \(\
abla\cdot U=S+\Omega\)--where \(S=\frac{1}{2}\Big{[}\
abla\cdot U+\left(\
abla\cdot U\right)^{T}\Big{]}\) is the rate-of-strain tensor and \(\Omega~{}=\frac{1}{2}\Big{[}\
abla\cdot U-\left(\
abla\cdot U\right)^{T} \Big{]}\) is the vorticity tensor--Q can be defined as \(\text{Q}~{}=\frac{1}{2}\Big{(}|\Omega|^{2}-|S|^{2}\Big{)}\). Considering this, the iso-surfaces of the Q-criterion vorticities are exhibited in Figures 12 and 13. Figure 3:0 Dependence of the non-dimensional recirculation width (\(W_{r}^{*}\)) on the Reynolds number. The vortex shedding overall is well-organized but not as regular as the classical Karman vortex. The length of the vortex varies differently as the net deformation changes. It is easy to capture the vortex shedding in the horizontal net twines rather than in the vertical ones, meaning that the horizontal net twines have less impact on vortex formation. Meanwhile, vertical net twines significantly affect vortex formation, leading to delayed vortex shedding. These vortices for \(Sn=0.16\) (Figures 12a-c and 13a,b) have proven that mutual interference does not exist in this situation. However, from Figures 12d-f and 13c,d, we see remarkable wake interactions for \(Sn=0.33\). In particular, the wake interacts more severely at the angles of attack between \(\pi/4\) and \(\pi/3\), and the considered Reynolds number is above 1200. This indicates that, when the net solidity \(Sn\geq 0.33\), there is significant interference between net twines that should not be neglected.