## 3 Results
### Turbulence Intensity Analysis  
The turbulence intensity reflects the momentum exchange characteristics on both sides of the interface caused by the motion of fluid particle. Larger turbulence intensity means more significant three-dimensional characteristics of the flow, and large-scale structures are easily broken into small-scale structures [43]. In order to further explore the relationship between the unique dynamic behavior of the vortex and the turbulent fluctuation characteristics of the flow field under RAM, the distribution of maximum turbulence intensity at intersecting surface versus the streamwise x-direction and its integration over the entire streamwise x-direction are compared and analyzed for the three cases, as shown in Figures 8 and 9, respectively. Figure 8: Peak value of turbulence intensity along streamwise direction for three cases: (**a**) \(RS11\); (**b**) \(RS22\); (**c**) \(RS12\); (**d**) \(TKE\). The turbulence intensity characterized by four indexes, including the dimensionless streamwise Reynolds normal stress (\(RS11\)), transverse Reynolds normal stress (\(RS22\)), Reynolds shear stress (\(RS12\)), and turbulent kinetic energy (\(TKE\)) are calculated as follows,  
\[RS11=\frac{\overline{\rho u^{\prime}u^{\prime}}}{\rho_{1}\Delta u^{2}} \tag{32}\]  
\[RS22=\frac{\overline{\rho^{\prime}v^{\prime}v^{\prime}}}{\rho_{1}\Delta u^{2}} \tag{33}\]  
\[RS12=\frac{\overline{\rho u^{\prime}v^{\prime}}}{\rho_{1}\Delta u^{2}} \tag{34}\]  
\[TKE=\frac{1}{2}\left(\frac{\widetilde{u^{\prime}u^{\prime}}+\widetilde{v^{ \prime}v^{\prime}}}{\Delta u^{2}}\right) \tag{35}\]  
Here, \(\overline{\rho}\) is the average density, \(\rho_{1}\) is the density of lower flow, \(u^{\prime}\) is streamwise pulsation velocity, \(v^{\prime}\) is transverse the pulsation velocity and \(\Delta u\) is the velocity difference between upper and lower flow. It can be seen that all the turbulence intensity characteristic values of the benchmark case have 'one peak'. The reason of 'one peak' is the roll-up of vortices in the flow field, and the strong shearing effect leads to large pulsations in the mixing layer, resulting in a peak in the turbulence intensity term at this location. Whereas, in both Case 2 and Case 3 two higher peaks are detected along the streamwise x direction due to the effect of incident and reflected shock waves. Previous researches demonstrated that this phenomenon of'multiple peaks' [44] can significantly promote the mixing process, so shock wave is beneficial to mixing augmentation. By comparing Case 2 and Case 3, it can be found that the growth rate of turbulence intensity is almost the same in both cases. However, under the influence of the RAM in case 3, the area where the shock wave impacts on the mixing layer is larger, which makes the turbulence intensity peak higher and the range of large values of turbulence intensity wider. This distribution property indicates that the RAM has a considerable effect on the large-scale enhancement of turbulence intensity in the mixing layer. Comparing the distribution of different turbulence intensity characteristics in the streamwise x-direction, it can be seen that the turbulence intensity of \(RS22\) reaches the peak earlier than that of \(RS11\) in Case 3, making the enhancement of the transverse Reynolds stress peak in this condition is not as significant as that of the streamwise Reynolds stress. This is because the shock oscillation is in streamwise direction in the RAM. Thus, the effect on the transverse Reynolds stress is not significant. The decline after \(RS12\) reaches its peak is gentler than that of \(RS22\). This is because the shear Reynolds stress is a combined measure of turbulent pulsations in both the streamwise and transverse directions, and the superposition of the streamwise delayed peak and the transverse trough  
Figure 9: Integration of turbulence intensity along the streamwise direction for three cases. makes the tangential Reynolds stress decrease more slowly.