## 4 Results and Discussion
### Aircraft Wake Vortices in Ground Effect with Crosswind
Furthermore, the crosswind velocity of magnitude U\({}_{\infty}\) = 0.04 makes the vortical structure from the right attain a maximum height of about 0.83 h during the loop; consequently, that vortical structure tends to leave the runway faster with sufficient intensity into the path of a smaller aircraft operating on a parallel runway. Figure 11: Trajectories of wake vortices with roughness effects: Re = 75,000 and \(\epsilon/\Delta\)s = 0.001 [21]. Figure 10: Trajectories of wake vortices with roughness effects: Re = 7650 and \(\epsilon/\Delta\)s = 0.001 [21]. The effects of the higher relative roughness height, i.e., \(\varepsilon/\Delta\)s = 0.007, are initially shown in Figures 12 and 13. The most important result for Re = 7650 is that crosswind of magnitude U\({}_{\infty}\) = 0.04 inhibits the primary vortical structure to loop a distance less than 0.875 B (Figure 12). That behavior can be linked with vertical shear effects because of surface roughness interaction with the primary vortical structures. In practice, the vertical shear provokes a change in the crosswind velocity as a function of the vertical coordinate; consequently, the extent of the rebound is also modified. The roughness effects are also able to change the form of a primary vortical structure without destroying it. The control of roughness height effects is important because the trajectory of primary vortices is quite modified. In Figure 13, the time evolution of the pair of primary vortical structures for test case 9 can be accompanied, as shown in Figure 5:0 The interference of the crosswind velocity of magnitude U\({}_{\infty}\) = 0.04 can be clearly visualized in Figure 13b when compared with Figure 5 (test case 1 in Table 1). The combination of the effects of crosswind with higher velocity and relative roughness with higher height pushes the vortical structures more quickly towards the runway on the right. The decay in wake vortices can also be visualized through numerical values present in the legend _\"Velocity Magnitude\"_ in Figure 13a-d.  
Another interesting result in Figure 14 shows that the combination of crosswind velocity of U\({}_{\infty}\) = 0.02 with a relative roughness height of \(\varepsilon/\Delta\)s = 0.007 at Re = 75,000 restores the condition for the primary vortical structure from right to loop, in which a maximum height of order of 0.78 h is then attained (Figures 11 and 14 can be compared). Figure 5:1 Trajectories of wake vortices with roughness effects: Re = 75,000 and \(\varepsilon/\Delta\)s = 0.007 [21]. Figure 5:2 Instantaneous velocity field distributions: Re = 7650, U\({}_{\infty}\) = 0.04 and \(\varepsilon/\Delta\)s = 0.007. An important observation is that decay in wake vortices is much more pronounced than the configuration with no crosswind and a smooth ground plane, when Figures 7 and 15d are compared through the legend _\"Velocity Magnitude\"_ at \(t\) = 50. In Figure 14, it can be clearly observed that crosswind interference combined with higher relative roughness height makes the loop higher as the crosswind velocity magnitude increases. As a consequence, the vortical structures' velocity magnitude will also decrease, i.e., the vortical structures encounter less difficulty in leaving the ground plane, being more easily blown by crosswind. Rough surfaces are proven to be able to control the flow separation of secondary vortical structures originating from the ground plane. Thus, the numerical results shown in Figure 14 seem to indicate that roughness effects are able to move the separation points downstream. Figures 11 and 14, when compared, show that the looping phenomenon in the primary vortical structure from the right and its subsequent movement leaving the runway depend on the features of roughness at a high Reynolds number of Re = 75,000. The surface roughness interference on the velocity field decay is clearly identified when the Reynolds number increases from Re = 7650 (Figure 13) to Re = 75,000 (Figure 15).