# Airplane Vortices Evolution Near Ground
## 4 Results and Discussion
### Flow Field Evolution under Crosswind Conditions  
The temporal flow evolution of the vortices' central core and surrounding area for different crosswind speeds and circulations is presented in Figure 24. Under crosswind conditions the entire flow-field also undergoes modifications. In order to see how it varies, the cases with a two-phase circulation temporary decay will be used in Equations (33), (34) and (36). At the initial time steps the flow evolution with and without crosswind is very similar; compare Figures 23 and 24. Once the time reaches \(t^{*}=0.5\) the differences start to be seen. At this time step, as the crosswind velocity increases, the perturbed flow field moves further to the right, and the area below the central core is particularly affected by the crosswind velocity where it generates a perturbed flow wedge that in the future times tends to wrap up the vortex central core. The central core flow field engulfment appears to be less relevant as the circulation increases; this is due to the higher flow field intensity associated with higher circulations.  
At the time step of \(t^{*}=1\), the central core wrapping up is clearly observed; the vortex's central core starts suffering a clear deformation and elongation due to the stresses generated by the crosswind velocity. The deformation increases with the circulation decrease (taking into account that the deformation of the vortex generated by the medium airplane is similar to the other ones, but the time elapsed is lower, because \(t_{0}\) is lower, see Table 5).  
For the last two time steps (\(t^{*}=1.5\) and \(t^{*}=2\)), the vortices under a crosswind velocity of 2 m/s present a very noticeable deformation, stretching the vortices and further elongating them, and the flow area upstream is completely swept towards the downstream direction. For the three different cases presented it is clearly seen how the crosswind deeply deforms the center of the vortex, passing from a round shape to an elliptical one. This mentioned degeneration is bigger as the time increases, and the deformation due to the ground effect can hardly be seen, and thus it loses relevance. What is particularly relevant to mention at the final time step presented is that the vortical structures have moved sideways (along the abscissa axis). The medium airplane vortices have moved, approximately, 110 m, and the ones of the heavy airplanes have displaced by almost 200 and 190 m for the case of the vortices generated at a higher altitude. The value for the same models but without considering crosswind is, approximately, 30, 75 and 40 m, respectively.  
Another aspect to be observed is the tendency of the particles to move together with the crosswind, instead of rotating together with the vortex, a characteristic that differs from the observations made for the case without crosswind (Figure 23). Additionally, in all of the cases the particles of the right side of the represented domain move further sideways to the right than the ones in the left side. The same happens when comparing the top to the bottom of the domain.  
Figure 24: The flow field representation has been performed for 5 time steps, which correspond (from top to bottom) to \(t^{*}=0\), 0.5, 1, 1.5 and 2. The ambient conditions include a crosswind equal to 2 m/s.  
One characteristic that has to be taken into account is that the boundary layer has not been represented in the near-ground domain, but in the real case could have some relevance for the crosswind movement, because the sideway movements of the particles touching the ground could generate new vortexes that could affect the motion of the principal ones.  
Finally, the main difference between the cases with and without crosswind resides in noticing that the ground effect, which was particularly relevant in the cases without crosswind, becomes quite irrelevant as the crosswind velocity increases.