## 1 Introduction  
Ski jumping performances often consist of four distinct phases, invn, take-off, flight, and landing, which involve ballistic and aerodynamic aspects. Both aspects impose specific requirements on ski jumpers, such as maximizing lift and minimizing drag. Ballistic factors include the jumper's take-off position and velocity from the take-off table, while aerodynamic factors encompass the aerodynamic characteristics of the jumper-skis system, including speed, posture, environmental wind, clothing, and ski length [1]. After the take-off phase, it is crucial for the athlete to assume a stable flying position as soon as possible early during the flight phase [2], minimize drag [3], and achieve a complete balance between backward and forward angular momentum rotations [4]. The flight phase is where the aerodynamic characteristics of ski jumping are most evident, and researchers have conducted studies on the aerodynamic characteristics during this phase using wind tunnel experiments, combined field measurements and numerical simulations, among other methods [5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19]. Computational fluid dynamics (CFD) is the preferred tool for visualizing and analyzing the flow field around the athlete, enabling the analysis of aerodynamic forces, pressure distribution, and detailed flow information during motion. CFD has been widely applied in various sports disciplines, including cycling [20], bobsledding [21], and race walking [22]. CFD is considered an important tool for future research on the aerodynamics of ski jumping [1], although current CFD studies in ski jumping mainly focus on the invn and flight phases [23; 24; 25; 26; 27; 28; 29; 30; 31]. [PERSON] et al. (2017) employed CFD to investigate the effects of the attack angle and velocity on aerodynamic forces, and their numerical results indicated that velocity had little influence on the lift and drag coefficients during the early flight phase, whereas variations in the attack angle had a significant impact on the lift and drag acting on the athlete [9]. Similarly, CFD studies have found that the aerodynamic characteristics of the skis play a more crucial role in the jumper-skis system and should not be overlooked while considering the athlete's posture [29]. Furthermore, environmental wind has a significant influence on the aerodynamic characteristics of ski jumping and the performance of athletes [32; 33; 34; 35; 36; 37; 38]. In addition, [PERSON] et al. (2019) explored the optimization of athlete posture under the influence of wind, where the optimal attack angle of the skis was smaller in headwinds and larger in tailwinds compared to no wind conditions. Under given flight technique constraints, the optimal body-to-skis angle was minimized, except for the final part of the flight, where a smaller angle could be employed to achieve greater jump distance, which is feasible under headwind conditions, albeit with increased difficulty in maintaining flight stability [39]. In summary, previous CFD studies on the aerodynamic characteristics of the flight phase in ski jumping have mainly focused on factors such as flight speed, attack angle, athlete posture, ski posture, and horizontal headwind or tailwind conditions, all under the assumption of symmetric athlete-skis system postures. However, flight stability is crucial for ensuring the performance and safety of ski jumping [40; 41]. In addition to environmental wind, the posture of the multi-body system is highly significant for controlling flight stability and is closely related to the performance of ski jumping. Nevertheless, little is known about the effects of unfavorable conditions. The term unfavorable conditions specifically refer to the flying scenarios under crosswind and asymmetric attitude conditions.