## 4 Partitioned Strong Coupling Formulation
The net with higher solidity shows less offset because of the net panel's increased shielding effect and weight. The largest offset reaches 0.078 m when the flow velocity is 0.75 m/s and \(Sn=0.16\). Figure 8 presents the magnitude of the flow velocity \(u\) along \(y\)-direction at different distances downstream of the net panel center. The velocity exhibits a U-shaped distribution in the overall range of \(-0.125\) m \(\leq y\leq 0.125\) m. However, the velocity along the \(y\)-direction at different angles of attack in [PERSON] et al. [13] is more likely a V-shaped distribution (see Figure 16 in [PERSON] et al. [13]). We note that the net panel being studied in [PERSON] et al. [13] does not consider the deformation; instead, by directly assigning different inclination angles, the authors examined the velocity distribution of an undeformed net panel. The deformation could be the cause of the differences in velocity distribution between the present study and [PERSON] et al. [13]. From Figure 8, we see distinct velocity reductions concerning different net solidities. Higher solidity causes greater velocity reduction, mainly because of the increased shielding effect. However, the relative difference in velocity reduction between these two net panels drops from 40% to 30% when flow velocities increase from 0.15 m/s to 0.75 m/s. This means that the velocity reduction differences between these two net panels become smaller as the flow velocity increases, because the shielding effect becomes weak when the inclination angle grows. Under this circumstance, the flexible nets choose to \"go with the flow\" to reduce the flow impact and reduce drag forces. We separately define the distances \(X=0.13\) m and \(X=0.50\) m as near-field and far-field, while \(X=0.25\) m is a distance in the middle of the near field and far field. The velocity reduction is larger in the near field than those beyond it. It appears that the velocity distribution in the middle of near field and far field is more stable than those in the near field and far field. Severe velocity fluctuations exist in the near field when \(Sn=0.16\). There is no interference between net twines at such a low solidity; however, the large opening in the net allows the flow to develop aggressively. Considering this, with blocking from the net twines, the severe velocity fluctuations appear in the near field. Furthermore, the velocity fluctuations become much more severe when the flow velocity rises to 0.6-0.75 m/s. There are also some obvious velocity fluctuations at a solidity of 0.33 if the flow velocity is over 0.6 m/s. Compared to the near-field velocity distribution, far-field velocity exhibits a zigzagged distribution, mostly because there are velocity gradients in the far field induced by the net deformation. Figure 8: The magnitude of the flow velocity \(u\) along \(y\)-direction at different distances downstream of the net panel center. Here, the flow velocities from top to bottom are from 0.15 m/s to 0.75 m/s with an increment of 0.15 m/s. ### Recirculation and Vortex Formation

Recirculation is a specific condition alongside flow separation from a bluff body. The flow separation immediately generates a low-pressure area that rolls the flow back into the body, resulting in a circulating vortex or pair of vortices. Therefore, it is necessary to quantify the recirculation and its size (e.g., width), given their close connections with the body pressure and the drag acting on the net panel. The recirculation creates remarkable variations in drag compared to those situations in which the flow remains attached to the surface of the body. Three typical sections on the net panels, namely the top, middle and bottom (Figure 9), have been selected to monitor the recirculation and vortex formation behind the vertical net twines. There is no need to monitor the horizontal net twines since they are always parallel to the flow direction. Figure 10 depicts two-dimensional instantaneous streamlines of three selected sections at different Reynolds numbers in the same time frame.