## 3 Experimental Results and Discussions
### PIV Measurement Results  
Besides the surface pressure measurement results, the PIV measurement experimental result can assist us in understanding the control mechanism of the trailing edge jets set in the SBG model. Turbulence kinetic energy (TKE), which serves as a criterion to estimate the unsteady surface pressure and the fluctuating aerodynamic force that is acting on the SBG model [31, 32, 33], is calculated as follows:  
\[\text{TKE}=\frac{\overline{u^{\prime 2}}+\overline{v^{\prime 2}}}{2U_{0}^{2}} \tag{6}\]  
where \(u^{\prime}\) and \(v^{\prime}\) are the fluctuating velocity components of the streamwise and transverse direction, respectively. The time-averaged flow fields behind the SBG model in the two target planes with and without the trailing edge jets are given in Figure 7. A cluster of large values of the TKE is concentrated in the wake flow when \(J_{sj}=0\), as shown in Figure 7a. The reason is that the separation flows from the upper and bottom surfaces interact in the wake, leading to the velocity vectors colliding in this region. Therefore, the surface pressure distribution nearing the trailing edge when \(J_{sj}=0\) shows a dramatic fluctuation. As the trailing edge jets is conducted in the SBG model, the distribution area and maximum value of the TKE are reduced. Moreover, the maximum value of the TKE decreases at first and then increases with the enhancement of \(J_{sj}\), as shown in Figure 7a-e, which can explain the changing trend of the fluctuation of the aerodynamic force that is being exerted in the SBG model. Compared to results from the target plane II, both the maximum value and the concentrated area of TKE in the target plane I of the case \(J_{sj}=0.0094\) is reduced as shown in Figure 7c.f. The unsteady aerodynamic force being exerted in the cross-section of plane I is lower than that of plane II, indicating the pressure measurement result that was obtained by plane II would underestimate the control effectiveness of a fluctuating value of surface pressure that is distributed on the SBG model with trailing edge jets. Moreover, the lower TKE value  
Figure 6: Time histories (**a**) and power spectrum analysis (**b**) of the lift force being exerted in the SBG model of cases \(J_{sj}=0\) and \(J_{sj}=0.0094\). illustrates that the level of turbulence mixing in the wake flow of the controlled cases is lower than the uncontrolled case [34]. The instantaneous flow field in plane I that is given in Figure 8 illustrates the vortex shedding pattern behind the SBG model. A pair of asymmetric vortices alternating shed from the upper and bottom surface of the SBG model and a Karman vortex street can be obtained in the wake flow, which causes the significant fluctuation of the surface pressure on the trailing edge of the test model without control, as shown in Figure 4. The position where the upper and lower vortices interact leads to the enormous TKE value, which can be seen when comparing Figures 7a and 8a. However, when the trailing edge jets work, a pair of symmetric vortices are formed in the wake flow field and the Karman vortex street is alleviated. The length of the vortex shedding is elongated and shifted further downstream, as given in Figure 8b. In addition, the jet flow interacts with the upper vortex and divides that vortex into some small-scale vortices, illustrating that the unsteady aerodynamic force that is being exerted in the SBG model is mitigated, and then the potential vortex-induced vibration can be prevented with the trailing edge jets [26]. At first, the proper orthogonal decomposition (POD) method was presented in the region of fluid mechanics by [PERSON] [35]. The snapshot POD that was introduced by [PERSON] [36] was utilized in the present investigation. Here, every instantaneous photo that was obtained by the PIV experiment served as a snapshot of the flow structure. The autocovariance matrix was accepted by the product of the matrix of fluctuating part of the two-dimensional velocity and its transpose.