# Effects of Bogies on the Wake Flow of a High-Speed Train
## 5 Results and Discussions
### Time-Averaged Flow Field
#### 5.2.2 Turbulent Kinetic Energy  
The TKE defined by Equation (16) is one of the most important variables used in the evaluation of the intensity of the turbulence in turbulent flow and it is directly related to the transport of momentum in the flow:  
\[T_{E}=\frac{1}{2}(\overline{u^{\prime}u^{\prime}}+\overline{v^{\prime}v^{ \prime}}+\overline{w^{\prime}w^{\prime}}), \tag{16}\]  
where \(u^{\prime}\), \(v^{\prime}\), and \(w^{\prime}\) are the fluctuation velocity components in the streamwise, spanwise, and vertical directions, respectively; the symbol \"--\" indicates the time average of the corresponding variables. The streamwise distributions of the time-averaged TKE at different locations of the wake of the three models are shown in Figures 14 and 15.  
A comparison of the streamwise TKE distributions in the wake of the three models at different span positions (\(y=0\), 0.875, 1.75, and 2.975 m) (Figure 14) indicates that the TKE distributions are  
Figure 14: Streamwise distributions of time-averaged TKE at different spanwise positions (z = 0.2 m): (a) real model, (b) semi-simplified model, and (c) simplified model.  
Figure 15: Streamwise distributions of time-averaged TKE at different vertical positions (y = 0.875 m): (a) real model, (b) semi-simplified model, and (c) simplified model.  
similar for the real and semi-simplified models. The TKE is large near the nose of the trailing car and at the spanwise middle of the wake (\(y=0\) and 0.875 m) and it monotonously decreases downstream of these two streamwise positions. At the position of \(y=2.975\) m, which is the outer side in the spanwise direction, TKE rises slightly and then gradually attenuates.  
However, the TKE distributions in the wake are quite different for the simplified model. The TKE at \(y=0\) is relatively small, whereas it is larger at \(y=0.875\) m. After the peak at \(x=45\) m, the TKE decreases monotonously downstream. For \(y=1.75\) m, which is the outer side in the spanwise direction, the TKE is small near the nose of the trailing car, then exhibits a significant increase, reaches a peak at \(x=57\) m, and finally gradually decreases. For \(y=2.975\) m, the TKE is almost zero. The TKE distributions at different spanwise positions are closely related to the movements of the vortex structures in the wake, and hence implies information about positions and incidences of vortices.  
The streamwise distributions of the TKE in the wake of the three models at different heights (\(z=0.2\), 0.305, 0.55, 1.04, and 1.95 m) are shown in Figure 15. It is observed that the TKE distributions in the wake are similar for the real and semi-simplified models. The largest TKE values occur near the nose of the trailing car and then the values monotonously decrease downstream. As the height increases, the TKE values decrease. However, the TKE distributions in the wake are different for the simplified model. At the positions of \(z=0.2\) and 0.305 m, except for the TKE peaks near the nose of the trailing car, another distinct peak is observed in the range of \(45\) m \(<x<50\) m. In addition, the TKE values no longer decrease as the height increases in the simplified model because the TKE at \(z=1.04\) m is larger than that at \(z=0.55\) m, whereas it is close to zero at \(z=\)1.95 m.