## 3 Distribution and Evolution of Vortex Structures
### Evolution of Vortex Structures in the Whole Process of VIV
The vortex distribution around the box girder in the gradual convergence stage is shown in Figure 7b. In this stage, vortex shedding also occurs on the leeward inclined web of the lower surface, with the size of 0.31 m, and because of the increase in the VIV amplitude of the box girder, the vertical motion of this vortex is more obvious and closer to the inclined web of the upper surface. On the upper surface, some vortex structures on the leeward roof dissipate and some vortex structures are captured by the vortex structures on the windward roof,  
Figure 8: Contours of time-averaged vortex structures at \(3\pi/2\) moment (Unit: s\({}^{-1}\)). **(a)** Rapid development stage of VIV. **(b)** Gradual convergence stage of VIV. **(c)** Stable vibration stage of VIV. so the size of the vortex on the windward roof increases to 0.54 m. It can be seen from Figure 7c that during the stable vibration stage, due to the downward movement of the box girder, the vortex attached to the leeward wind fairing moves upward to the top of the wind fairing. The size of the vortex on the windward side of the upper surface continues to increase to 0.47 m. Meanwhile, vortex shedding occurs on the leeward side, and the vortex size on the leeward roof is only 0.18 m. The vortex shedding process on the leeward side of the top surface is virtually complete, and the huge vortex is positioned on the middle and front of the upper surface, while the large vortex on the lower surface will fall off at this time, according to the comparison. At 3\(\pi\)/2 moment, the vortex distribution at different stages of VIV is shown in Figure 8. The little vortex on the leeward inclined web of the top surface has dropped off, the size of the vortex on the leeward roof increases to 0.65 m, and the size of the vortex on the windward roof decreases to 0.13 m, as shown in Figure 8a. The vortex behind the leeward inclined web of the lower surface has moved far behind the box girder. As shown in Figure 8b, in the gradual convergence stage, the vortex on the upper surface is divided into two parts by the central guardrails, and the size of the two sub-vortex structures is 0.14 m and 0.29 m, respectively. The vortex behind the leeward inclined web on the lower surface has also fallen off. The vortex on the leeward wind fairing has dropped off the surface in the steady vibration stage, and the little vortex on the leeward roof of the top surface flows backward and is spread through the leeward railing, as shown in Figure 8c. Furthermore, the vortex on the top surface's windward side goes to the leeward side, which is prevented by the central guardrails, with just a small portion of the vortex reaching the leeward roof. It can be concluded that the large vortex structures on the upper surface of the box girder are located on the leeward roof in the first two stages of VIV, while the motion of the vortex structures in the stable vibration stage lag behind, the vortex structures are still on the windward roof. In conclusion, the scale and distribution of vortex are obviously different in different stages of VIV, and the motion of vortex structures in the stable stage lag behind the other two stages. During the upward movement of the box girder, the vortex shedding occurs at the tail of the upper surface, and the size of vortex structures at the lower surface increase. Vortex shedding happens at the tail of the lower surface during the downward movement of the box girder, and the size of vortex formations at the upper surface increases. In addition, combined with the flow field distribution, it can be found that the incoming flow is blocked by the wind fairing, railings, and other structures, resulting in vortex structures at the leading edge of the box girder. The source of the vortex is the shape parameters of the windward side of the box girder, including the angle of the wind fairing, the height, and spacing of the railings.