## 5 Conclusions  
A Lagrangian vortex method algorithm was developed to blend large-eddy simulation (LES) theory with a surface roughness model. The viscous effects were computed through the corrected core-spreading method, in which vortex blobs were not treated as fluid material particles; otherwise, \"convergence errors\" would be identified. The local eddy viscosity coefficient was computed together with the vorticity diffusion solution from Equation (12). The local second-order velocity structure function of the filtered field was used to compute the eddy viscosity coefficient from Equation (4), also enabling the implementation of the roughness model from Equation (8). The roughness model once again proves to be efficient since it has already been applied to study bluff body aerodynamics in high Reynolds number flows by Lagrangian vortex method [7; 8]. The method was applied to aircraft wake vortices evolving close to the rough ground plane with crosswind. The following conclusions were obtained:  
1. Lagrangian vortex interactions with combined effects of crosswind and surface roughness were efficient in simulating the enhanced dissipation of aircraft vortex wakes in the vicinity of a runway. 2. The effect of aircraft wake vortices separating and rebounding upon interacting with the runway was successfully captured. 3. The formation of the boundary layer on the ground and the subsequent generation of secondary vortical structures were the key effects responsible for the rebound; thoses phenomena were simulated in a very good physical sense. 4. A comparison of trajectories of primary vortical structure between experimental data and numerical results presented a good agreement at Re = 7650 (Figure 6). The experimental data included the effects of the lateral wall for the recirculation water tank. 5. The crosswind velocity of magnitude U\({}_{\infty}\) = 0.04 combined with relative roughness height of \(\varepsilon/\Delta\)s = 0.001 at Re = 75,000 caused the primary vortical structure to attain a maximum height of about 0.83 h during the loop; importantly, vortical structures tend to leave the runway faster with sufficient intensity to disturb a smaller aircraft operating on a parallel runway (Figure 11). * The decay in aircraft wake vortices, which are leaving a rough ground plane, is more pronounced than configuration with no crosswind and smooth ground plane, when, as an example, Figures 7 and 15d can be compared through numerical values shown in the legend _\"Velocity Magnitude\"_ at \(t=50\). * The control of roughness height appeared to be a determining factor to interfere with the trajectory of primary vortices generated by a large aircraft approaching or leaving a ground plane with crosswind. * The numerical results confirmed that extensive data and CFD are required to develop wake models linked with systems such as _\"Wake Turbulence Re-categorization_ or _Wake RECAT\"_ (a safe decrease in separation standards between aircrafts). Conceptualization, G.F.M.d.C., M.F.V. and L.A.A.P. ; data curation, G.F.M.d.C., M.F.V. and A.M.B. ; formal analysis, G.F.M.d.C., A.M.B. and L.A.A.P. ; funding acquisition, L.A.A.P. ; investigation, G.F.M.d.C., M.F.V. and A.M.B. ; methodology, A.M.B. and L.A.A.P. ; project administration, G.F.M.d.C. and L.A.A.P. ; resources, G.F.M.d.C. and L.A.A.P. ; software using Fortran, G.F.M.d.C. and M.F.V. ; validation, G.F.M.d.C., M.F.V. and A.M.B. ; visualization, G.F.M.d.C. and L.A.A.P. ; supervision, L.A.A.P. ; writing--original draft, L.A.A.P. ; and writing--review and editing, G.F.M.d.C., A.M.B. and L.A.A.P. All authors have read and agreed to the published version of the manuscript. The authors would like to thank FAPEMIG (a research supporting foundation of Minas Gerais state), project no. APQ-01246-23; and the Sao Paulo Research Foundation (FAPESP), grant no. 2022/03630-4, for their financial support. Not applicable. The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy and ethical restrictions.