# Numerical Study of Aircraft Wake Vortex Evolution under the Influence of Vertical Winds
## 1 Introduction  
As the number of flights in China continues to increase yearly, many airports are gradually reaching their capacity limits, leading to increasingly severe flight delays. Aircraft taking off and landing on the same runway or on closely spaced parallel runways (where the lateral spacing between runways is less than 760 m) must maintain a minimum safe separation distance to avoid the adverse effects of wake turbulence from preceding aircraft [1]. Therefore, reducing wake turbulence separation intervals has become an important research focus for improving aircraft takeoff and landing efficiency and airport capacity [2; 3]. The evolution and decay of aircraft wake vortices are closely related to the surrounding atmospheric conditions. Research has shown that wind disturbances can affect the propagation and dispersion of wake vortices [4]. In particular, vertical wind directly impacts the structure, vortex strength, decay rate, and altitude of the vortex core, which subsequently affects wake turbulence separation and the extent of the danger zone. Therefore, it is essential to conduct detailed research on the evolution and detection of wake turbulence in vertical wind conditions, which is necessary for establishing dynamic wake turbulence separation criteria under different atmospheric backgrounds. Research methods for aircraft wake turbulence primarily include wind tunnel experiments, laser radar measurements, theoretical modeling, and computational fluid dynamics (CFD) [5]. 1. Wind Tunnel Experiments: Wind tunnel testing is a traditional method of studying aircraft wake turbulence. It involves creating scaled-down physical models of airplanes and observing wake turbulence effects. However, the atmospheric environment's complexity and the measurement equipment resolution limitations restrict thismethod's precision. Wind tunnels also have limits when studying the long-distance development of wake vortices [6]. * Laser Radar Measurements: Laser radar systems are employed for wake turbulence observations. These systems use lasers to measure various properties of wake vortices. However, their effectiveness can be limited by atmospheric conditions and measurement range [7; 8; 9]. * Theoretical Modeling: Theoretical models are used to predict the behavior of wake turbulence based on mathematical equations and principles. These models provide valuable insights into wake vortex characteristics, but they may have limitations when capturing all the complex interactions in real-world conditions [5; 10]. * Computational Fluid Dynamics (CFD): CFD is a computational method that simulates fluid flow based on fundamental physical principles. It offers high scalability, strong visualization capabilities, and the ability to conduct simulations for various aircraft types under different flight phases and atmospheric conditions. In recent years, CFD has found extensive applications in aircraft wake turbulence research and prediction [11; 12]. CFD simulations can provide valuable insights into the behavior of wake vortices, their evolution, and the effects of different atmospheric conditions, including wind. This computational approach allows researchers to conduct extensive and detailed studies that can be challenging or impossible to achieve through other methods [13]. Scholars use different turbulence models to numerically simulate the formation of the wake vortex and the evolution of the near-field stage. [PERSON] et al. simulated the initial formation and subsequent evolution of the wake vortex through the Reynolds-averaged Navier-Stokes (RANS) approach and assessed the safety interval between different models in the terminal area through the intensity of the wake vortex [14]. [PERSON] and colleagues utilized adaptive mesh-based Large Eddy Simulations (LES) to analyze the near-ground evolution of vortices in the wake of the ARJ21 aircraft, initialized using a lift-drag model.