## 4 Correspondence of Vortex Structures and Vortex-Induced Pressures
### Relation between Vortex Structures and VIPs at the Stable Stage of VIV  
The distribution and development of vortex at each step of VIV of the box girder were examined in the preceding section. The VIPs are illustrated by red lines in Figure 9, which illustrates the distribution of vortex and VIPs at eight points in a vibration cycle during the stable stage of VIV. At 0 moment, several small vortex structures generate on the leading edge of the upper surface and windward roof, and the VIPs are positive at the corresponding areas. There is a huge vortex in the middle and rear part of the upper surface, which tends to move backward, causing negative pressure with a large absolute value. At 5\({}^{\circ}\) wind attack angle, the flow field around the lower surface of the box girder is relatively stable, and the vortex-induced pressure on the windward inclined web and bottom plate of the lower surface is positive. There is obvious vortex shedding on the leeward inclined web of the lower surface, which leads to negative pressure with a larger absolute value. At \(\pi/4\) moment, compared with the previous moment, the huge vortex on the upper surface continues to move backward, and has passed through the central guardrails to the leeward lane, and the corresponding peak value of VIPs also moves backward. The absolute value of negative pressure on the leeward inclined web of the lower surface decreases because the shedding vortex continues to move away from the region, and the change of vortex and VIPs in other parts is not obvious. At \(\pi/2\) moment, the large vortex on the leeward side of the top surface moves backward and tends to break away, and the peak value of the VIPs in this region decreases. Several small vortex structures on the windward side of the top surface have merged to form a larger vortex, and the VIPs in this region are still positive, and the pressure value increases slightly. Although there is a region with obvious vorticity at the right rear of the leeward inclined web on the lower surface, the vorticity field and streamline in this region do not change significantly, so the corresponding VIPs do not change significantly. Figure 9: _Conts._  
The enormous vortex on the windward side of the upper surface remains nearly motionless during the downward movement of the box girder, and the positive pressure in this region progressively declines. The enormous vortex on the leeward side of the top surface dissipates, and the forward flow bypasses the large vortex structures on the windward side of the upper surface, acting directly on the leeward roof, resulting in a large positive pressure. The amount of the residual vortex in the roof's back end is modest, resulting in a considerable amplitude of positive pressure in this area. The positive VIPs in this location are caused by vortex structures on the top surface's leeward inclined web. On the lower surface's leeward inclined web, new vortex structures appear, and the accompanying VIPs change from negative to positive. At \(3\pi/2\) moment, the large vortex on the upper surface moves backward, but the main structure of this vortex is still located on the windward roof due to the obstruction of the central guardrail, and the VIPs of the windward roof area change from positive to negative. Only a small part of the vortex moves to the leeward roof, and the positive VIPs in this area decrease. The size of vortex on the leeward inclined web of the lower surface continues to increase, and the corresponding positive VIPs increase. At \(7\pi/4\) moment, the vortex on the upper surface continues to move backward, the main structure has been located on the leeward roof, and the VIPs in this area change from positive to negative. The vortex on the windward roof will break away from the surface of the box girder and will continue to bypass the central guardrail and move backward. Therefore, the absolute value of the negative pressure here is reduced, and some positions are subjected to positive VIPs.