## 3 Experimental Results and Discussion
### Particle Image Velocimetry for Characterizing the Flow Field
The pattern shown in Figure 13 is different from the pattern in Figure 11, except at the high \(F^{+}\) of \(Re=4.2\times 10^{5}\) and \(5.7\times 10^{5}\). For a low \(F^{+}\), a large value of the \(C_{L}\) increase ratio is also found for \(Re=5.7\times 10^{5}\) at \(F^{+}=0.5\) or 1.0; however, the ratio of the shear layer height is close to zero, and there is a small increase in the TKE in this region. This reasoning is insufficient to fully comprehend these phenomena. Figure 14 shows the normalized displacement of the boundary layer separation point with and without actuation, i.e., the fourth index. The region with a higher value of this index illustrates that the boundary layer separation at the leading edge is suppressed by the DBD-PA actuation, and the attached area is clearly extended, especially at \(Re=4.2\times 10^{5}\) and \(5.7\times 10^{5}\). In these red areas, the separation point of the boundary layer moves downstream, and the acceleration of the flow near the leading edge is enhanced. Thus, the negative \(C_{p}\) around the leading edge increases and \(C_{L}\) is enhanced, as shown in \[K_{CL}=\frac{C_{L}}{C_{L_{NoDA}}}-1, \tag{3}\]1 One of the reasons for the increase in \(C_{L}\) caused by plasma actuation in the red area in Figure 14 is the shift in the separation point of the boundary layer downstream. A comparison of Figures 13 and 14 illustrates that the red area in Figure 14 and the blue area in Figure 13 for \(Re=4.2\times 10^{5}\) and \(5.7\times 10^{5}\) are not in identical positions. That is, the  
\[K_{CL}=\frac{C_{L}}{C_{L_{NoDA}}}-1, \tag{3}\]2 PIV results of vorticity fields and velocity vectors for typical flow fields with DBD-PA actuation. changes in each index are similar in the high \(F^{+}\) region but different in the low \(F^{+}\) region. The disturbance generated by the DBD-PA increases the momentum of the boundary layer near the leading edge of the wing at a specific \(Re\) without depending on \(F^{+}\). Therefore, it effectively suppresses the boundary layer separation without attracting the shear layer. These results imply that the increase in \(C_{L}\) caused by DBD-PA actuation is attributed to three phenomena that occur individually or in combination:  
1. Increases in TKE in the shear flow on the suction side of the wing. 2. Momentum recovery in the flow field on the wing caused by the shear layer being attracted to the wing surface. 3. Acceleration of the flow around the leading edge. In (1), a high TKE indicates the presence of high-energy vortices generated in the shear layer. The low pressure area caused by the rotation of these vortices can improve the wing lift. In (2), DBD-PA actuation places disturbances and vortices into the shear layer, promoting momentum exchange between the mainstream and recirculation zones, resulting in momentum recovery. In addition, momentum recovery occurs when the shear layer moves to the wing surface because of the movement of the separation point of the boundary layer downstream on the suction side of the wing owing to the disturbance or acceleration by DBD-PA actuation. These two momentum recovery methods cause an increase in the \(C_{L}\). In (3), the DBD-PA actuation enhances the disturbance in the boundary layer at the leading edge of the wing, and such a disturbed boundary layer is more resistant to flow separation, enabling a longer distance for the boundary layer attachment. Thus, a longer distance results in a large negative \(C_{p}\) area around the leading edge, thereby increasing \(C_{L}\).