## 4 Results and Discussion
### Evolution Mechanism of Flow Field
#### 4.3.2 Local Flow Field  
To examine the distinct mechanisms governing falling debris flight both in single-train and trains-crossing scenarios, seven key instants (\(t_{1}\)\({}^{\prime}\)-\(t_{7}\)\({}^{\prime}\)) during debris descent are analyzed for transient flow field evolution. Figure 17 illustrates the debris surface vortex structure using the Q-criterion (\(Q\) = 10,000), with turbulent kinetic energy (\(TKE\)) coloring the vortices. Figure 18 depicts surface streamlines colored by relative velocity (\(CRV\)). Definitions of \(TKE\) and \(CRV\) are given in Equations (10) and (11), respectively.  
\[TKE=\frac{3}{2}(\overline{U}I) \tag{10}\]  
\[CRV=(U_{air}-U_{trains})/V \tag{11}\]  
where \(\overline{U}\) represents the average wind speed of the air, \(I\) represents the air turbulence, \(U_{air}\) represents the wind speed of the grid center point, and \(U_{trains}\) represents the translation velocity of the grid center point.  
As depicted in Figures 17 and 18, under both single-train and trains-crossing conditions, a similar characteristic vortex structure is observed around the falling debris. During the initial flight phase (from \(t_{1}\)\({}^{\prime}\) to \(t_{2}\)\({}^{\prime}\)), the scale of this peripheral vortex structure remains relatively small, resulting in aerodynamic forces stabilizing near zero. Over time, the characteristic vortex scale expands while its density increases, imparting force for both translational and rotational motion of the debris. Concurrently, turbulent kinetic energy (\(TKE\)) near the debris rises due to heightened turbulence around the train body. This augmentation in vortex structure and \(TKE\) induces temporal fluctuations in the aerodynamic coefficients of the falling debris.  
In comparison to the single train driving condition, the vortex structure near the falling debris is characterized by a smaller scale and a higher number under the trains crossing condition. Notably, moments such as \(t_{6}\)\({}^{\prime}\) and \(t_{7}\)\({}^{\prime}\) exhibit a small aerodynamic coefficient and a considerable fluctuation range. Except for instances at \(t_{2}\)\({}^{\prime}\) and \(t_{4}\)\({}^{\prime}\), vortex structures on the surface of the falling debris are also observable under the single train condition, predominantly in the -\(X\) direction of the falling debris. Consequently, this results in a greater impulse on the falling debris and a longer flight distance in the \(X\) direction.  
The \(CRV\) at the edge of the falling debris is generally larger than that at the center, which makes a circle of characteristic vortex structure appear at the edge of the falling debris. Over time, the \(CRV\) exhibits an increasing trend, leading to a gradual enlargement of the vortex structure on the surface of the falling debris. In contrast to the single train driving condition, the \(CRV\) under trains crossing condition is smaller, resulting in a correspondingly smaller vortex structure. Moreover, an examination of the surface streamline reveals a more intricate flow field under the intersection conditions. For instance, at the \(t_{2}\)\({}^{\prime}\) moment, multiple cores are evident on the upper surface streamline of the falling debris under trains-crossing conditions, whereas only one core is present under the single-train conditions. A similar phenomenon can be observed at \(t_{2}\)\({}^{\prime}\). This complexity is a primary factor contributing to the generation of numerous small-scale vortices near the falling debris under trains-crossing conditions.  
Figure 17: Vortex structure evolution on the falling debris surface: (**a**) XZ view; (**b**) XY view; (**c**) \(ZY\) view.  
Figure 18: Flow field evolution on the falling debris surface: (**a**) top surface; (**b**) bottom surface.