## 4 Numerical Study
### Effectiveness Investigation  
In order to investigate the effectiveness of \"fishnet\" in erosion reduction, the scouring behavior of tidal current around the monopile foundation before using the \"fishnet\" technology was investigated for comparison. Herein, Tecplot was employed to display the calculated streamlines. This is because ANSYS-CFX-CFD-Post can only display the streamlines of the whole model or a single surface, whereas Tecplot can display the local three-dimensional streamlines separately. The streamlines of the flow around the monopile are shown in Figure 8.  
Figure 6: An example of the meshing results: (**a**) isometric view; (**b**) top view.  
Figure 7: Boundary conditions.  
From Figure 8, it can clearly be seen that the direction of tidal currents changes when they reach the monopile. In detail, downflow formed in front of the monopile, particularly in the region close to the seabed where tidal currents had slower speeds. Horseshoe vortices and annular acceleration current flow can clearly be seen on the side of the monopile, and pairs of counter-rotating vortices can also be observed behind the monopile.  
After installing a \"fishnet\", characterized by \(l\) = 40 cm, \(d\) = 5 cm, and \(H\) = 3.5 m, on the monopile, the streamlines of the tidal currents were re-calculated. The results are shown in Figure 9.  
Although it is difficult to observe the effect of the fishnets from Figure 9, it can clearly be found from Figure 9 that small vortices were generated by the fishnets, which disturbed the original flow field and, thus, affected the downflow and the vortices around the monopile.  
Although the streamlines in Figure 9 successfully indicated the working mechanism of the fishnets, they were still unable to demonstrate the effect of \"fishnet\" in erosion reduction. It is known that seabed erosion happens only when the shear stress on the seabed exceeds a critical value [23]. For this reason, the shear stress on the seabed around the monopile foundation was calculated before and after adopting the \"fishnet\" technology. The calculation results are shown in Figure 10.  
Figure 8: Streamlines of tidal current when passing the monopile foundation.  
Figure 9: Streamlines after using the fishnet: (**a**) side view; (**b**) details of the flow in front of the monopile.  
From Figure 10a, it can be found that the shear stresses on both sides of the monopile were much larger than those in other areas, meaning that the left and right sides of the pile were more susceptible to erosion, and that scour pits were to be produced there first. From Figure 10b, it can be found that, after using the fishnet device, the shear stresses on both sides of the monopile were significantly reduced. Before using the \"fishnet\" technology, the maximum shear stress on the surface of the nearby seabed was 1.179 Pa. The maximum shear stress on the surface of the seabed decreased to 1.012 Pa after the \"fishnet\" technology was adopted. In other words, the maximum shear stress was reduced by 14% after using the proposed technique.  
Finally, considering that eddy viscosity can be used to characterize the transport and dissipation of the energy of the vortices around the monopole [25], the eddy viscosities before and after using the fishnets were calculated. The results are shown in Figure 11.  
From Figure 11, it can be seen that a pair of vortices occurred behind the monopile, which corresponded to the trajectory of the tail vortices. Before using the \"fishnet\" technology, the maximum eddy viscosity was 3.317 Pa. The maximum shear stress on the surface of the seabed decreased to 3.255 Pa after the \"fishnet\" technology was adopted. Although such a reduction in the maximum eddy viscosity was not obvious, the comparison of Figure 11a,b shows that the tail vortices were significantly suppressed by the fishnets.