# Numerical Study of Aircraft Wake Vortex Evolution under the Influence of Vertical Winds
## 3 Results
### Analysis of Wake Vortex Parameters
#### 3.3.1 Analysis of Wake Vortex Parameters under Different Wind Directions  
Figure 14 represents the horizontal position distributions of the vortex core under different positive and negative wind speeds (favorable wind denotes wind blowing from above, while adverse wind denotes wind blowing from below). From Figure 14, it can be observed that under calm wind conditions, the vortex core steadily contracts inwards. Under positive wind speeds of 1 m/s and 2 m/s, the vortex core briefly contracts inwards before stabilizing and oscillating. Specifically, under 2 m/s wind speed conditions, the vortex core spacing is smaller than under 1 m/s wind speed conditions. Under negative wind speeds of 1 m/s, the vortex core steadily contracts inwards at a rate 1.5 times that of still air conditions. At the x/c = 7 cross-section, the horizontal displacement of the vortex core matches that of still air conditions; under negative wind speeds of 2 m/s, the vortex core contracts inward steadily for a distance before rapidly contracting inwards and stabilizing. This phenomenon is known as the detachment of secondary vortices. When wind speeds increase, the airflow kinetic energy within the primary vortex increases. The vortex core may be influenced by wind speed gradients and rotation rate gradients, resulting in the instability of the primary vortex and irregular motion and interaction within the vortex core structure. This can lead to the detachment of the vortex core from the primary vortex and the formation of secondary vortices. Figures 15 and 16 display the horizontal position of the secondary vortex core and vorticity cloud maps at different places behind the wing. At the x/c = 5 cross-section, the vorticity of the primary and secondary vortex is consistent. However, the vorticity decay rate and horizontal position change in the two vortices show different trends. The vorticity of the secondary vortex decays more rapidly, and by the x/c = 15 cross-section, it has attached itself to the outside of the primary vortex and merged with it. The horizontal position reduction in the secondary vortex is consistent with the conditions under \(-\)1 m/s wind speed. From Figure 17, it can be observed that under still air conditions, the vortex core exhibits a slight tendency to curl upward, which is in line with the findings of [PERSON]'s wind tunnel experiments on near-field wingtip vortices, as documented in the literature. The vortex core tends to move upward and outward in the initial stages relative to the wingtip. This phenomenon is attributed to the \"knotting\" effect generated by the fusion of the primary vortex and secondary vortices. Under favorable wind speed conditions, the vortex core steadily moves downward, with a rate 2.25 times that of 1 m/s under 2 m/s wind speed conditions. Under adverse wind speed conditions, the vortex core steadily  
Figure 14: Horizontal position distribution of the vortex core under different wind directions. Figure 18 illustrates the vertical and axial velocity distributions at the vortex core under different wind speeds (results are non-dimensionalized using the inflow velocity in the x-direction). The vertical rate at the vortex core fluctuates around \(-\)1 m/s. Vertical wind increases the vertical velocity at the vortex core, with a more significant effect as wind speed increases. The absolute value of the rate increases with the downstream distance. Under a wind speed of 4 m/s, at the x/c = 10 cross-section, the vertical velocity at the vortex core reaches nearly 20 m/s. Vertical wind near the vortex interacts with the surrounding air, leading to collisions and momentum exchange. This, in turn, alters the dynamic pressure and enhances turbulence in the flow field near the vortex core, resulting in increased vertical velocity. Under calm wind conditions, the axial speed at the vortex core fluctuates around 70 m/s, maintaining consistency with the aircraft's forward rate. In vertical wind, the axial velocity at the vortex core increases with more incredible wind speeds.