## 3 Results and Discussion
### Analysis of PIV Experimental Results
(**a**) Instantaneous flow field of Case 0; (**b**) Instantaneous flow field of Case 4; (**c**) Time-averaged flow field of Case 0; (**d**) Time-averaged flow field of Case 4. TKE: turbulence kinetic energy. Figure 12 shows results of the test models at the angle of 15\({}^{\circ}\) that are similar to those at the angle of \(-20^{\circ}\). In comparison with the Case 0 results, TKE values are greatly reduced and the recirculation regions are obviously smaller in size. As for the two-dimensional incompressible flow, the vorticity in the \(z\) direction can be written as:  
\[\omega_{z}=\frac{\partial v}{\partial x}-\frac{\partial u}{\partial y} \tag{5}\]  
where \(x\) and \(y\) are the coordinates along the downstream direction and vertical flow direction. According to Equation (5), both the vortex motion and the shearing motion are identified by the vorticity in the flow, the vortex forming and shedding locations cannot be clearly identified to represent the flow. To get rid of the shearing motions, we used the imaginary part of the complex eigenvalue of the velocity gradient tensor to distinctly visualize vortices [32]. Since the two-dimensional flow velocity fields are obtained through the PIV measurements, the full velocity gradient tensor cannot be formed, and we can only set up a two-dimensional form of the velocity gradient tensor [33] as:  
\[D_{\mathrm{2-D}}=\left[ \begin{array}{cc}\frac{\partial u}{\partial x}&\frac {\partial u}{\partial y}\\ \frac{\partial v}{\partial x}&\frac{\partial v}{\partial y}\end{array} \right] \tag{6}\]  
Figure 12: Instantaneous and time-averaged flow fields for Case 0 and bypass jet control at a wind attack angle of 15\({}^{\circ}\). (**a**) Instantaneous flow field of Case 0; (**b**) Instantaneous flow field of Case 4; (**c**) Time-averaged flow field of Case 0; (**d**) Time-averaged flow field of Case 4. We conducted a detailed experiment focusing on the wake flow behind the test model to investigate the formation of passive jet flow. Here, we adopted swirling strength as the indicator to reveal the jet vortex, as shown in Figures 13a and 14a. It should be noted that the measurement resolution increased to 1.4 mm \(\times\) 1.4 mm in this case. It can be observed that there are streamlines being evacuated out from the bypass system into the model wake, as shown in Figures 13 and 14. The quantitative analysis of the separation points and the recirculation sizes was then performed, with results shown in Figure 15. The size of the recirculation region is not obvious according the streamlines and vortices; therefore, we conducted an analysis of the velocity profiles near the model surfaces. The blue solid line in Figure 15 in the revised manuscript represents the zero point line of the velocity distribution, and the velocity in the horizontal direction of the position of the model surface separation point is zero. According to these blue lines, we determined the separation points of the flow from the model surfaces. Moreover, the distances between the blue lines and the model surface will reflect the size changes of the recirculation regions. Because 99 \(\times\) 74 vectors are shown in the fields, the uncertainty may increase by an additional 1/99 \(\times\) 100% = 1% in the horizontal direction and 1/74 \(\times\) 100% = 1.4% in the vertical direction under the resolution of PIV measurements. When the  
Figure 14: The instantaneous and time-averaged flow fields for the by-pass jet control at wind attack angle of \(-20^{\circ}\). (**a**) Instantaneous flow field of Case 4; (**b**) Time-averaged flow field of Case 4. Figure 13: The instantaneous and time-averaged flow fields for the by-pass jet control at wind attack angle of \(15^{\circ}\). (**a**) Instantaneous flow field of Case 4; (**b**) Time-averaged flow field of Case 4.  
wind attack angle was \(-20^{\circ}\), the flow separation point was X/B = 0.208 away from the leading point for Case 0, while it was delayed to X/B = 0.226 for Case 4.