# The Refined Simulation Methods of Fluctuating Wind and Aerodynamic Forces Relative to Moving Trains
## 4 The Fluctuating Wind Simulation of Moving Trains
### The Fluctuating Wind of Moving Trains  
It is easy to generate the time histories of fluctuating wind relative to moving trains with the derived wind spectra and the harmonic wave superimposing method. Set the speed of the train at 250 km/h, and the wind direction angle is \(\varphi_{0}=90\) degrees. The train starts to move from the \(x=0\) position at moment \(t=0\) s. With the parameters defined in Section 4.1 and the same random phases, the fluctuating winds of moving trains in the four different wind environments described in Table 1 are simulated, as shown in Figure 5.  
Considering the inhomogeneous characteristics of the wind environment, the fluctuating wind speed relative to the moving train decreases significantly by comparing Figure 5b with Figure 5d. In addition, the fluctuating wind speed near \(t=14.4\) s is almost unchanged; this is because as the train moves to the position of \(x=~{}1000\) m at \(t=14.4\) s, the mean wind speed on the train reaches the maximum in the inhomogeneous wind environment. Comparing Figure 5c with Figure 5d, it can be seen that the fluctuating wind speed of the moving train is almost unchanged in the vicinity of \(t=30\) s, taking the non-stationary  
Figure 4: Comparison of derived wind spectra with that proposed by [PERSON] et al. (2023) (Ref. [10]).  
characteristic of the wind environment into account, while it is significantly reduced in other time ranges. The reason for this phenomenon is that the modulation function is 1.0 at \(t=30\) s, and the mean wind speed on the train reaches the maximum in the non-stationary wind environment.  
Overall, the fluctuating wind of moving trains is more likely to be affected by the inhomogeneous characteristics of the wind environment because it shows significant decreases in the inhomogeneous wind environment. Since a train with a speed of 250 km/h passing through a 2000 m inhomogeneous wind field only needs 28.8 s, the wind speed acting on the train could reach the maximum at \(t=14.4\) s. However, wind speed reaches the maximum at \(t=30\) s in the non-stationary wind environment. That is to say, the high-speed train is more affected by the inhomogeneous wind field within a short period.  
Figure 5 illustrates the difference in the simulated fluctuating wind under different wind environments. It can be seen that wind environments characterized by inhomogeneity and non-stationarity have significant effects on the fluctuating wind relative to moving trains. The natural winds in canyon areas would have prominent inhomogeneous characteristics in the range of hundreds of meters [2], and they only show significant non-stationary characteristics after a few minutes [23]. However, high-speed trains could travel a long distance in a short period. Therefore, the inhomogeneous characteristic of the natural wind has a more significant effect on the wind field relative to moving trains in tens of seconds. Existing methods for fluctuating wind simulation pay more attention to the general wind environment, but the proposed method in this study has broader applicability, especially in inhomogeneous and non-stationary wind environments, such as canyon areas.  
Figure 5: Along-wind fluctuating wind relative to moving trains under different wind environments: (**a**) inhomogeneous and non-stationary wind environment; (**b**) inhomogeneous and stationary wind environment; (**c**) homogeneous and non-stationary wind environment; and (**d**) homogeneous and stationary wind environment.