## 3 Experimental Results and Discussion
### Particle Image Velocimetry for Characterizing the Flow Field
Furthermore, the value shows a ridge at \(F^{+}\) between 10 and 100 with \(Re\) between 4.2 \(\times\) 10\({}^{5}\) and 5.7 \(\times\) 10\({}^{5}\). The following discussion focuses on the phenomena that cause the characteristics of this index, as shown in Figure 11, based on the dependence of the other three indices on \(Re\) and \(F^{+}\). Figure 11: \(C_{L}\) increase ratio. Figure 12: Maximum TKE increase ratio. Figure 12 shows a contour map of the increase ratio of the maximum TKE by DBD-PA actuation, which is referred to as the third index in the previous section. According to Figure 12, the \(F^{+}\) of the point where the value of the index is the largest exists between 0.1 and 1.0 for each \(Re\) number condition and decreases drastically with an increase in the \(Re\) number. This result implies that higher energy vortices are effective in producing larger disturbances and turbulence with an increase in the \(Re\) number, similar to the flow energy. The energy of each vortex is related to the input energy allocated to each burst wave when the vortices originate from the burst actuation of the DBD-PA. In this study, the time-averaged input power for all experimental conditions was uniform; therefore, a greater input energy was allocated to a single burst wave in the case of a smaller \(F^{+}\). Consequently, a higher \(Re\) number requires a smaller \(F^{+}\) value to achieve a larger TKE. Furthermore, Figure 15a,b show the instantaneous vorticity fields and velocity vectors at \(Re\) = 1.9 \(\times\) 10\({}^{5}\) with \(F^{+}\) = 1 and at \(Re\) = 4.2 \(\times\) 10\({}^{5}\) with \(F^{+}\) = 0.5, respectively. Under both conditions, the maximum TKE increase ratio exhibits a high peak (Figure 12). Both flow fields are observed under DBD-PA actuation with a low \(F^{+}\), indicating that one or two vortices with a large negative vorticity are shed into the shear layer formed by the boundary layer separation near the leading edge. Both flow fields are frequently observed  
Figure 14: Normalized displacement of the separation point of the boundary layer on the wing model with and without DBD-PA actuation. \[K_{CL}=\frac{C_{L}}{C_{L_{NoDA}}}-1, \tag{3}\]0 Ratio of the shear layer height. in the instantaneous PIV results under both conditions, which supports the consideration of high-energy vortices generated by DBD-PA actuation. The PIV data in this study had an insufficient time resolution; therefore, further studies using high-speed PIV or a phase-locked method are required to directly confirm from the PIV results that these vortices are generated synchronously by DBD-PA actuation. Considering the region where the third index is high, a comparison of Figures 11 and 12 illustrates that the conditions of \(Re\) and \(F^{+}\) with indices greater than 1.5 are relatively close in the bottom-left region in these figures. In contrast, from the same comparison at the region where the third index is less than 1.5, the first index increase found in the previous paragraph is not fully accounted for by the ridge of the third index, e.g., at \(Re=4.2\times 10^{5}\) with \(F^{+}=10\), \(Re=5.7\times 10^{5}\) with \(F^{+}=50\), and \(Re=5.7\times 10^{5}\) with \(F^{+}=0.5\) and 1.0. Figure 13 highlights the effectiveness of the DBD-PA based on the change in the shear layer height behind the separation point with and without actuation, i.e., the second index. The blue region in this figure, where the shear height ratio is negative, indicates a flow field in which the momentum of the flow near the wing surface recovers because the shear layer approaches the wing. Figure 13 illustrates that a higher \(F^{+}\) effectively changes the velocity profile of the shear layer and recovers the momentum on the wing surface compared to a lower \(F^{+}\); the values of the most effective \(F^{+}\) are within 10 and 50. A higher \(C_{L}\) increase ratio can be obtained by increasing the momentum around the wing, i.e., a higher negative value of the shear layer height ratio.