## 5 Results
### Three Important Flow Features and the Guidelines from the Observations  
Another interesting feature that may be related to the existence of the third group is shown in Figure 9a,b, where the _L/D_ dependence on the burst frequency \(F^{+}\) is plotted for NACA0015 and NACA0006 airfoils, respectively. The figures show that a higher frequency (\(F^{+}\) = 6.0) is more effective for achieving a higher _L/D_ for the NACA0015 (a thick airfoil) as has already been described, while a lower frequency (\(F^{+}\) = 1.0) is more effective for the NACA0006 (a thin airfoil) independent of any actuator locations and values of _Dc_. There thus occurs another question: Why does a low burst frequency (\(F^{+}\) = 1.0) work better for a thin airfoil such as NACA0006, while a high frequency such as \(F^{+}\) = 6.0 works better for a thick airfoil such as NACA0015? It should be noted that the values of _Dc_ in Figure 9a,b are much smaller than those in Figure 7. Although the Reynolds number was same, the _Dc_ values in our early simulations shown in Figure 7 were determined based on the longer chord and lower freestream velocity, which are different from those in the experiment described here. As a result,  
Figure 8: Aerodynamic performance versus rapidity of turbulent energy promotion in the chordwise direction: \(\alpha\) = 12\({}^{\circ}\), _Re_ = 6.3 \(\times\) 10\({}^{4}\)[14]. the \(Dc\) values became large and the region of the DBD plasma actuator was small (relative to the model scale). We confirmed, however, that same conclusion was also obtained for the smaller \(Dc\) values. An analysis of the instantaneous flow fields, phase-averaged flow fields, frequency spectrum, and linear stability of the separated shear layer was performed. Such effort led to identifying a few different representative flow features [39; 46]. As has been described, the turbulent transition turned out to be one of the most important factors for the flow separation control at this Reynolds number. To further confirm this estimation and find appropriate burst parameters for better flow control, the linear unstable modes in the separation shear layer profile and the spatial growth rates were investigated [40; 47]. The most unstable frequency was approximately \(S_{t}=15\) in the separated shear layer flow structure when the DBD plasma actuator was off. Here, \(S_{t}\) is the non-dimensional frequency defined by the chord length and the freestream velocity. The most unstable frequency was approximately \(S_{t}=35\). when the DBD plasma actuator was turned on. The DBD plasma actuator in the burst mode creates two-dimensional spanwise vortices at the beginning and at the end of every bursting. They merge together and a stronger two-dimensional vortex with the same frequency as \(F^{+}\) is eventually appears. This implies that the vortices created initially for the case of \(F^{+}=6.0\) have a Strouhal number similar to the unstable frequency \(S_{t}=15\). Higher-frequency components are also created, so low input frequencies such as \(F^{+}=1.0\) would have similar frequencies as harmonics, but the higher input frequency \(F^{+}=6.0\) has much higher power spectrum density components at the most unstable frequency than \(F^{+}=1.0\). This might be why actuation is more effective for \(F^{+}\) around \(6.0\) than for \(F^{+}\) around \(1.0\) at this angle of attack. A similar analysis was conducted for the flow separation control by the synthetic jets [47; 48]. Here, strength of the induced flows is not too important, but the frequencies of the disturbance introduced by the DBD plasma actuator are important. A two-dimensional vortex created by the burst mode actuation described above is another important feature that plays an important role in the flow separation control. Such flow structures were found in the time sequence of the flow fields obtained through the phase and spanwise averaging of the simulation data. They were also experimentally observed. Figure 10a-d shows an instantaneous snapshot of the PIV particle images in several cases [38].