## 3 Experimental Results and Discussion
### Particle Image Velocimetry for Characterizing the Flow Field  
In this study, the velocity field on the negative pressure side of the wing was observed using a PIV method at a 24\({}^{\circ}\) AoA. The mechanism by which the DBD-PA actuation controls the flow field and the increase in \(C_{L}\) was investigated in more detail using this visualization. This AoA was adopted because there are conditions of \(F^{+}\) with a peak of \(C_{L}\) increase at angles of attack of 20\({}^{\circ}\)-25\({}^{\circ}\) for all \(Re\), as shown in Figure 8f-h. Investigating these conditions enabled us to determine the mechanism of flow control with high efficiency. Both the second and third flow patterns, represented as the red and blue areas in Figure 8a-d, respectively, were present at \(\sim\)24\({}^{\circ}\). Investigating these conditions enabled us to determine the flow control mechanism for different positions of the boundary layer separation. Furthermore, a 24\({}^{\circ}\) AoA was carefully selected to ensure that \(C_{L}\) was less affected by the hysteresis caused between the up- and down-sweep motions of the AoA, regardless of the flow pattern and \(Re\), as shown in Figure 6.  
Figure 9a,b illustrate the distributions of the time-averaged \(x\)-component of the flow velocity, \(\overline{u}\), and turbulent kinetic energy (TKE), respectively. These were calculated from 1000 image pairs of instantaneous velocity distributions measured using PIV. The conditions were \(F^{+}\) = 1 with \(Re\) = 9.4 \(\times\) 10\({}^{5}\). The direction of the main flow was from left to right, and the wing model is shown in these images up to 66% of the chord length. Figure 9a shows that the separation point of the boundary layer is estimated as 0.16c; furthermore, it shows that the wing surface is covered by a recirculation zone. A shear layer, shown as a change in contour color in Figure 9a, is formed between the main flow and the recirculation. This layer overlaps with a region with a large TKE value, as shown in Figure 8(b). This TKE region starts immediately upstream of the separation point of the boundary layer. The shear layer thickness is shown in Figure 8(a), which is defined as the distance between the position of \(u/u_{\infty}=0\) and the outer edge of the shear layer at a certain chord position. The high-TKE regions in Figure 8(b) become wider with an increase in the distance from the separation point downstream. In this study, the characteristics of the flow field were investigated by calculating the following four indices using the velocity, TKE, and \(C_{L}\) data. (1) The \(C_{L}\) increase ratio \(K_{CL}\): this index was calculated by normalizing the \(\Delta C_{L}\) with the \(C_{L}\) without DBD-PA actuation in the same flow condition. The \(K_{CL}\) is defined as follows:  
\[K_{CL}=\frac{C_{L}}{C_{L_{NoDA}}}-1, \tag{3}\]  
where \(C_{L}\) and \(C_{L_{NoDA}}\) are the lift coefficient with and without DBD-PA actuation at a 24\({}^{\circ}\) AoA, respectively. A total of 28 data points were calculated considering all \(F^{+}\) and \(Re\) number conditions in this study. (2) The ratio of the shear layer height \(K_{h}\): to calculate the ratio of the shear layer height, the \(\xi\) axis was defined in the direction parallel to the chord line of the wing, and the \(\eta\) axis was defined in the direction perpendicular to the \(\xi\) axis, considering the origin of the coordinates at the leading edge of the wing, as shown in Figure 8(a). Figure 8(a) shows the velocity profile of the \(\xi\)-component along the axis parallel to this \(\eta\) axis on the wing surface obtained at \(\xi/c=0.2\), 0.325, and 0.45. The momentum thickness was calculated at several \(\xi/c\) values, and the shear layer height was defined as the momentum thickness at \(\xi/c=0.45\). The change in the momentum thickness with respect to the chord direction was approximately linear.