## 4 Conclusions  
In this paper, we research the mixing enhancement characteristics induced by the strategy of WJISW in a supersonic flow field through large eddy simulations. The instantaneous flow structures, turbulence pulsation characteristics, mixing layer growth process, and modal decomposition results are obtained and analyzed. In order to accentuate the mixing enhancement effect of this strategy, the free mixing layer under the same conditions is compared with it. The following conclusions can be drawn:  
1. WJISW makes the mixing layer deflected. In particular, WJISW in a low frequency condition can result in the movement of the interaction position between NIP and FIP in the flow field. This new mode never reported before can be defined as'region action mode' (RAM). In this mode, the vortex structures exhibit unique dynamic \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Order** & **Proportion** & **Frequency/Hz** & **Growth Rate** & **Frequency/fj** \\ \hline
1 & 0.05807 & \(-2\times 10^{-10}\) & \(-7.69\) & 0 \\
2 & 0.01402 & 6018 & \(-94\) & 1 \\
3 & 0.00703 & 12,028 & 10 & 2 \\
4 & 0.00413 & 18,055 & 67 & 3 \\
5 & 0.00243 & 73,954 & \(-239\) & 12.32 \\
6 & 0.00239 & 24,025 & \(-300\) & 4 \\
7 & 0.00234 & 67,617 & \(-511\) & 11.26 \\
8 & 0.00229 & 186,742 & \(-225\) & 32.12 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Modes’ characters of the first eight modes in Case 3.  
behavior, including breakdown and deformation. This is significantly different from the flow field of the mixing layer induced by a wedge shock generator;
2. The turbulence intensity of the mixing layer under WJISW appears multi-peak in the streamwise x-direction, which can significantly promote the mixing process. In addition, WJISW in a low frequency condition can make the turbulence intensity peaks higher in the streamwise x-direction and the range of large values wider, indicating that the'region action mode' found in this paper has a considerable influence on the increase of turbulence intensity in the mixing layer, which significantly enhances the turbulent pulsation in the flow field;
3. The growth characteristics of the mixing layer under WJISW in a high frequency condition are similar to that of the mixing layer induced by wedge studied previously. The mixing layer thickness decreases after the shock interaction point, while the growth rate increases downstream, and eventually the mixing layer thickness will catch up with the free mixing layer. In contrast, under WJISW in a low frequency condition, the velocity thickness of the region where the shock wave acts with the mixing layer increases sharply, making the final velocity thickness increase by 62%, compared with the free mixing layer, and it greatly improves the mixing level;
4. The modal decomposition results show that the shock-induced modes dominate the flow field under WJISW. The coexistence of large- and small-scale structures in the mixing layer under WJISW in a low frequency condition is due to the dominance of the shock-induced modes. The entrainment and engulfment of large-scale structures promote surrounding fluids into the mixing region, and the nibbling effect of the small-scale structure facilitates the expansion of the surface area of scalar contact in the mixing layer, accelerating the exchange of mass, momentum, and energy between the upper and lower layers of the flow, both of which can effectively promote the mixing process;
5. The proposed strategy well shows the potential application in Scramjet and RBCC combustors for hypersonic propulsion systems. The newly observed'region interaction mode' in the flow field influenced by wall-jet induced shock waves can obviously accelerate the mixing process. Future work concerning the optimization is essential to obtain a deeper understanding of the proposed strategy. Conceptualization, D.Z. and Y.W. ; methodology, J.Z. and D.Y. ; validation, J.Z. and Y.W. ; writing--original draft preparation, J.Z. ; writing--review and editing, D.Y., Y.W. and D.Z. ; visualization, D.Y. and Y.W.