## 4 Numerical Study
### Optimization of \"Fishnet\" Technology  
Since the size and installation of the fishnet device may significantly affect the effectiveness of the proposed technology, the erosion reduction effect when the fishnet device had different settings of \(l\), \(d\), and \(H\) was investigated so as to obtain an optimal design of the device. The parameters used in  
Figure 11: Eddy viscosities: (**a**) before using the fishnet device; (**b**) after using the fishnet device.  
Figure 10: Shear stress on the surface of the seabed: (**a**) before using fishnet; (**b**) after using fishnet.  
different scenarios are listed in Table 2. In all of these scenarios, the fishnet had a thread angle of 45\({}^{\circ}\). The values of the maximum shear stress obtained in the different scenarios are shown in Figure 12. In the figure, size \"0\" implies that there was no fishnet on the monopile.  
From Figure 12, it can be found that, before using the fishnet device, the maximum shear stress on the seabed was 1.176 Pa. After using the fishnet device, the maximum shear stress was more or less reduced. When the size of the fishnets was increased from 20 cm, the value of the maximum shear stress decreased first and reached the minimum value of 1.01 Pa when the size was 40 cm, and then increased again with the continual increase in fishnet size. In comparison to the maximum shear stress obtained before using the fishnet device, the value of 1.01 Pa obtained when the size was 40 cm implies a reduction by about 14%. Thus, it can be said that fishnet had the best protective effect when the size of the fishnets was 40 cm.  
After obtaining the optimal size of fishnet, the effect of the diameter of the fishnet thread on erosion reduction was investigated, and the results are shown in Figure 13. In the calculations, the size of the fishnets was 40 cm, and the length of the fishnet device was 3.5 m. The diameters of the fishnet thread considered were 5 cm, 7.5 cm, 10 cm, 12.5 cm, and 15 cm.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Size of Fishnet** & **Diameter of Fishnet Thread** & **Length of Fishnet Device** \\ \hline \hline \(I\) **(cm)** & \(d\) **(cm)** & \(H\) **(m)** \\ \hline \hline Without fishnet & & \\ \hline
20 & 5.0 & 0.5 \\
30 & 7.5 & 1.0 \\
40 & 10.0 & 3.5 \\
50 & 12.5 & 5.0 \\
60 & 15.0 & 7.5 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Scenarios considered in simulation calculations.  
Figure 12: Influence of the fishnet size on the maximum shear stress on the surface of the seabed.  
From Figure 13, it can be seen that, with the increase of the diameter of the fishnet thread, the maximum shear stress on the seabed showed a generally increasing tendency. This suggests that a smaller diameter of the fishnet thread results in more scouring being mitigated. In comparison to the maximum shear stress of 1.176 Pa before using the fishnet device, the maximum shear stress dropped to 1.01 Pa when the diameter of the fishnet thread was 5 cm, which indicates a reduction of 14%.  
Finally, the influence of the length of the fishnet device on erosion reduction was investigated when the size of the fishnets was 40 cm and the diameter of the fishnet thread was 5 cm. The lengths of the fishnet device being considered in the investigation were 0.5 m, 1 m, 3.5 m, 5.5 m, and 7.5 m. The calculation results obtained in different scenarios are shown in Figure 14.  
From Figure 14, it can be found that, when the length of the fishnet device was increased, the value of the maximum shear stress decreased first, reached the minimum value of 1.01 Pa when the length of the device was 1 m, and then increased again with the increasing length of the fishnet device. This suggests that the optimal length was 1 m.