# Computational Study on Rogue Wave and Its Application to a Floating Body
## 3 Results and Discussion
### Bull's-Eye Waves Simulation
As the incident waves overlapped at the focal point, a wave with a high wave height was observed. A transient wave height was shown at first, and then it was slightly lowered, and a constant rogue wave was repeated. The crest was higher than the trough. The height difference between the crest and the trough increased as the amplitude at the inlet boundary increased. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Grid System** & **Number of Mesh in** & **Total Number** \\ \hline
**Index** & **Description** & **Wavelength/Wave Height** & **of Meshes** \\ \hline
1 & Coarse mesh & 63/12 & 784,672 \\
2 & Medium mesh & 80/16 & 1,486,953 \\
3 & Fine mesh & 100/20 & 2,800,530 \\
4 & Extra fine mesh & 126/24 & 5,324,560 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Grid sizes for grid convergence test. Figure 6: Time history of rogue wave’s elevation at focal point for four grids. Figure 8: Simulated rogue wave height. Figure 7: Relative errors between the four grids. Figure 9: Simulated rogue wave profile at \(x=0\) plane. Figure 11 shows the rogue wave's development over time. The contours showed the z-elevation at the iso-surface with a volume fraction of 0.5. The vertical white column indicates the focal point. The incident wave propagated from the inlet boundary to the focal point, and the rogue wave was generated. The rogue wave was observed at the focal point. Figures 12 and 13 show the wave profile at the \(y=0\) plane and \(x=0\) plane, respectively. In the \(y=0\) plane, the rogue wave was generated at the focal point and dissipated in  
Figure 11: Z-elevation contours of rogue waves (the vertical white column refers to \(x=0\), and \(y=0\)): (**a**) \(t/T=4\); (**b**) \(t/T=6\); (**c**) \(t/T=6.5\); (**d**) \(t/T=7\). Figure 10: Time history of rogue wave’s elevation at focal point. For the regular wave heights of 0.02, 0.03, and 0.04, the slopes were 0.0062, 0.0093, and 0.0124, respectively. In the rogue wave, the slopes were 0.024, 0.036, and 0.051 for the wave heights of 0.024, 0.036, and 0.051 on the inlet boundary, respectively. The rogue wave had a significantly increased asymmetry and slope compared to the regular wave. The pressure change due to the rogue wave was investigated. Figure 14 shows the pressure contours of water particles in the \(y=0\) plane for the regular and rogue waves. The wave height used at the inlet boundary of the regular and rogue waves was 0.02 m. In the regular wave, the pressure was in the range of \(-\)95.3-98.6 Pa, whereas in the rogue wave, the pressure was in the range of \(-\)216.6-568.9 Pa. When the rogue wave was generated by overlapping the regular waves, the pressure could increase by about six times, which could act as an important design factor for a floating structure. The effect of the rogue wave on the velocity of water particles was investigated. Figures 15 and 16 show x-velocity and z-velocity contours in the \(y=0\) plane for the regular and rogue waves, respectively. The wave height used at the inlet boundary of the regular and rogue waves was 0.02 m. In the regular wave, the x-direction velocity ranged from \(-\)0.0578 to 0.0648 m/s, whereas in the rogue wave, the x-direction velocity increased to the range from \(-\)0.104 to 0.202 m/s. The x-velocity increased about three times in the direction of the wave propagation and about two times in the opposite direction. In the z-velocity contours, z-velocity was in the range of \(-\)0.0438-0.0437 m/s in the regular wave, whereas the z-velocity was in the range of \(-\)0.216-0.195 m/s in the rogue wave. The z-velocity of the rogue wave was wider than that of the z-velocity of the regular wave. The maximum z-velocity increased about five times, which increased the wave height. The velocity vector at the interface of air and water phases for the regular and rogue waves was investigated. Figure 17 represents the velocity vectors at the free surface, which were captured from the volume fraction of 0.5.