# Numerical Study of Aircraft Wake Vortex Evolution under the Influence of Vertical Winds
## 1 Introduction
Their results showed that the horizontal tail vortex is the weakest and dissipates rapidly, while the wingtip vortex is the strongest and leads to a fusion with the horizontal tail vortex. Furthermore, the comparative analysis suggested that traditional wake vortex models can be applied to study the far-field evolution of wake vortices [15]. Different turbulence models and solver settings of RANS have been previously performed to investigate the accuracy of near-field wingtip vortices. The numerical simulation results show that the vortex core trace can be obtained more accurately when the spatial dispersion in the numerical calculation is larger than the fifth order by comparing the numerical simulation results with the wind tunnel experimental results of [PERSON] [16; 17] and colleagues, who conducted a three-dimensional numerical study to investigate the influence of fixed and moving wall boundary conditions on aircraft aerodynamic characteristics and wake vortex development. The results indicate that fixed walls overestimate the ground's viscous effects, leading to a reduction in the magnitude of the wingtip vortex (WTV). Additionally, the secondary vortex flow is induced by the wingtip and horizontal tail vortex (HTV) [12]. Numerous studies by scholars worldwide have explored the effects of different meteorological and ground conditions on the formation and evolution of wake vortices. [PERSON] and [PERSON] et al. [18] investigated the development of wake vortices under temperature stratification and other crosswind conditions through numerical simulations of non-constant two-dimensional laminar flow. They analyzed the changes in wake vortex trajectories under different weather conditions. [PERSON] and [PERSON] et al. [19] obtained 288 in situ wake vortex measurements and the respective environmental conditions by various detection systems. They found that side winds and turbulence affect the decay of the wake vortex and that side winds accelerate the decay rate of the downwind vortex. [PERSON] and colleagues conducted numerical simulations using an Euler-Euler multiphase flow model to investigate the evolution of wake vortices under different rainfall rates. The results indicated that rainfall accelerates the decay of wake vortices, reduces the tendency for velocity distribution within the vortex core to become smooth, alters the wake vortex's de scent pattern, and impacts the trajectories and concentration distribution of raindrops [20]. [PERSON] and [PERSON] et al. proved that the ground effect accelerates the attenuation of the tail vortex by statistically analyzing the actual detection data and gave a model of tail vortex attenuation under the ground effect based on the former model [19]. [PERSON] and colleagues, employing the Open FOAM solver, conducted Large Eddy Simulations (LES) to investigate aircraft wake behavior. The numerical simulation findings revealed the emergence of secondary vortex structures due to interactions between the wake and ground obstacles. These secondary vortices propagate outward along the vortex axis. Furthermore, the dissipation of the wake was found to vary following the distinct shapes of the ground obstacles [21]. [PERSON] et al. have established a tail vortex dissipation model, a motion model, and adopted the mirror vortex method to assess the strength of the ground effect according to the degree of increase in the spacing of the vortex nuclei, which better reflects the influence of the ground effect on the motion and dissipation of the tail vortex [22]. [PERSON] [23] conducted Large Eddy Simulations (LES) to investigate an unusually long-lived wake vortex phenomenon observed in their test program. This behavior is associated with the environmental crosswind's first and second vertical derivatives. This article aims to study the impact of vertical wind (both in direction and speed) on the structure and characteristic parameters of aircraft wake vortices during the near-field phase.