## 3 Experimental Results and Discussions
### Linear Stability Analysis  
[PERSON] et al. [39] found that the absolute instability of the flow field behind a bluff body is the reason for the vortex appearing in the wake of a stationary bluff body. The time-averaged streamwise velocity profiles, that were extracted from the mean flow field at various locations as shown in Figure 11a, substitute into the inviscid Orr-Sommerfeld equation (OSE). It should be noted that the higher-order small-term occurring in deducing the Orr-Sommerfeld equation and the viscidity of the air is neglected. Solving the OSE obtains the critical value in the complex frequency plane and the stability of the velocity profile by using the mathematical method that was presented by [PERSON] [40]. The imaginary part of the complex frequency, named as \(\omega_{i}\), determines the stability of the flow structure behind the SBG model. A positive \(\omega_{i}\) represents an unstable flow structure because the  
Figure 12: Reynolds stress distributions at different positions behind test model. (**a**) X/B = 0.03, (**b**) X/B = 0.12, (**c**) X/B = 0.21, and (**d**) X/B = 0.30.  
slight disturbance would evolve over time, leading to a large unstable flow structure [20]. Contrary, the small initial disturbance would vanish with time for a negative \(\omega_{i}\). Figure 13 presents the dispersion relation \(\omega=\omega(\alpha)\) maps \(\alpha_{i}\) constant lines on the \(\omega\) plane that were obtained by solving the OSE using the velocity profile at the position \(X/B=0.08\) of case \(J_{\text{\tiny{$S$}}}=0\). The \(\alpha\) is the complex wave number, and the \(\alpha_{i}\) is the imaginary part of \(\alpha\). The imaginary and real parts of the complex frequency at the cusp point are 0.31 and 1.75, respectively. This indicates the velocity profiles behind case \(J_{\text{\tiny{$S$}}}=0\) at \(X/B=0.08\) is absolute instability, causing the TKE to exhibit a considerable value in the wake flow, as shown in Figure 7a. According to the real part of \(\omega\), the Strouhal number of the wake flow can be calculated as 0.28, which is close to that which is gained by using the power spectral density analysis for the lift force that is acting on the SBG model as given in Figure 6b.  
The \(\omega_{i}\) at various locations behind the SBG model with and without trailing edge jets are obtained as given in Figure 14. It can be observed that the ranges of the absolute instability are stretched to the position of \(X/B=0.103\) for the case \(J_{\text{\tiny{$S$}}}=0\). The flow field was slightly stable at the near-wake, and the unstable region was broader for cases \(J_{\text{\tiny{$S$}}}=0.0016\), 0.0409, and 0.0802. However, for the case \(J_{\text{\tiny{$S$}}}=0.0094\), the unstable area was narrowed to \(X/B=0.029\), indicating the unstable range decreased about 71.84% compared to that of the case \(J_{\text{\tiny{$S$}}}=0\) as shown in the grey region of Figure 14. This phenomenon demonstrates that too strong jet flow isn't needed for controlling the unstable flow field of the SBG model with a trailing edge jet. An appropriate jet-speed causes a steadier flow structure behind the bluff body, which is also uncovered by [PERSON] et al. [41] in investigations of suppressing unsteady aerodynamic force that is being exerted in a circular cylinder. Therefore, a steady flow structure would excite the lower fluctuating amplitude of the aerodynamic force that is acting on the SBG model, as given in Figure 5. Moreover, the stability of the wake flow of the case \(J_{\text{\tiny{$S$}}}=0.0094\) is similar to that of the studies of leading-edge suction and trailing-edge jet (LSTJ) that are presented by [PERSON] et al. [20]. The superiority of the present control scheme is that the energy consumption of the case \(J_{\text{\tiny{$S$}}}=0.0094\) is half of that of the control method of LSTJ because the present control method only needs the trailing edge jets, not the leading-edge suction.