## 3 Results and Discussion
### Wake Flows  
Figure 16 shows the instantaneous iso-surface of the second invariant of the velocity gradient Q = 20,000 s\({}^{-2}\) simulated with different turbulence models at positions \(t_{1}\) and \(t_{3}\) coloured using the resultant velocity \(U\). Figure 16a presents the iso-surface of Q at position \(t_{1}\). A pair of twin counter-rotating longitudinal vortices (\(V_{1}\) and \(V_{2}\) or \(V_{1}\)\({}^{\prime}\) and \(V_{2}\)\({}^{\prime}\)) were observed for all three cases. However, the iso-surface of Q calculated by different turbulence models was found to be significantly different. Among them, the SST k-\(\omega\) model could not capture small-scale vortices. However, a large number of small-scale vortices were observed in the SA\(-\)IDDES and SST\(-\)IDDES models, and more small-scale vortices were captured with the SST\(-\)IDDES than with the SA\(-\)IDDES, particularly in the near-wake region. Figure 16b shows the iso-surface of Q at position \(t_{3}\). The \(V_{1}\)\(-\)\(V_{1}\)\({}^{\prime}\) region was induced by the interaction of two wake vortices on the intersection side. With the SST k-\(\omega\) model, the interaction between the two wake vortices in this region was strong and resulted in an 'entanglement' phenomenon. A similar phenomenon was also observed in the simulations using the SA\(-\)IDDES and SST\(-\)IDDES models. Furthermore, the flows in this region exhibited strong turbulence. For vortices \(V_{2}\) and \(V_{2}\)\({}^{\prime}\), the SA\(-\)IDDES and SST\(-\)IDDES models resulted in the formation and development of the vortex structures, and their intensity gradually decreased until they dissipated with the increasing distance from the tail car. However, because the RANS model dissipated the turbulent eddy viscosity, it could not resolve the small vortices [PERSON], et al. (2018). Therefore, we did not observe small-scale vortices at distances from the tail car larger than 7.58 H in the SST k-\(\omega\) model. Next, the streamlines projected on the vertical plane were used to study the local interaction of wake vortices as two MTs pass each other. Figure 17 shows the streamlines computed by different turbulence models in the plane X/H = 0 at \(t_{2}\) and \(t_{3}\). The vertical planes were coloured by the dimensionless longitudinal velocity (\(U_{x}=u/u_{tr}\)). The wake vortex of a single train travelling without crosswind is symmetrically distributed ([PERSON], 2016; [PERSON], 2016; [PERSON], 2016). However, Figure 17 shows that the interaction between vortices \(V_{c1}\) and \(V_{c1}\)\({}^{\prime}\) on the intersection side causes vortices \(V_{c1}\) and \(V_{c2}\) (or \(V_{c1}\)\({}^{\prime}\) and \(V_{c2}\)\({}^{\prime}\)) to be asymmetric. This phenomenon is observed with three turbulence models. The two vortices \(V_{c1}\) and \(V_{c1}\)\({}^{\prime}\) on the intersection side interact, causing their intensity to decrease and their width to be much smaller than that of the vortices on the non-intersection side. To provide a more quantitative comparison of the size of longitudinal vortices, the height of the vortex on the intersection side was denoted as \(h_{0}\), and the height and distance of the vortex core on the intersection side were denoted as \(h_{1}\) and \(w\), respectively, which is similar to the definition of [PERSON] et al. (2016), as shown in Figure 17b. Figure 17a shows the streamlines at position \(t_{2}\). It is evident that the turbulence model has minimal effect on wake vortices \(V_{c2}\) and \(V_{c2}\)\({}^{\prime}\) on the non-intersection side. However, vortices \(V_{c1}\) and \(V_{c1}\)\({}^{\prime}\) on the intersection side obtained by different turbulence models are significantly different. Figure 18 compares the \(h_{0}\), \(h\), and \(w\) values for the different models at different moments.