## 1 Introduction  
Flow control using a dielectric barrier discharge plasma actuator (PA) has been widely studied for the last 10 to 20 years because PA has the advantages of thin/light simple structures and easy to use. PA only consists of two electrodes with a dielectric layer between them (Figure 1), and can be attached to an existing body surface without changing the original shape of the body surface. PA can be attached on flat or curved surfaces, corners, or edges and flow separation is controlled [1; 2; 3]. PA is also used for the control of boundary layer flows [4; 5; 6; 7; 8; 9] and many researchers have tried to reduce skin friction drag by PA. To enhance the authority of PA, studies for PA expand over wide areas of research: low-temperature plasma discharge, flow structures induced by PA, use of duty cycles, etc. Geometry of the electrodes and the layout of multiple PAs were also studied. A good review of different types of PAs was written by [PERSON], [PERSON], and others [10], where review papers for conventional use of flow control by PA were presented. Up to the present, there has been active research on the application of various types of PA in a variety of devices [11; 12; 13]. For the flow separation control over an airfoil, PA is installed near the leading edge on the suction side of the airfoil surface except for in a few cases [14]. Most of the studies used a two-dimensional spanwise electrode, which induces coherent spanwise jet flows. Some studies used effective duty cycles (so-called burst actuation compared to regular continuous actuation), where still more effective flow control is achieved by a proper choice of the PA parameters. When duty cycles are used, two-dimensional coherent discrete vortex structures are induced at every cycle of the duty. Thus, PAs--especially in the burst actuation--have three important flow features: jet flow near the airfoil surface, two-dimensional vortex structures with the merger of these structures, and introduction of flow disturbances. Good authority of PA comes from the fact that each of these features may become dominant with proper choice of electric parameters [15]. Furthermore, in the flow control for airfoil flows, saw-tooth, serpentine spanwise electrodes, or line up of the chordwise electrodes--which create chordwise vortex structures and others--were studied by several authors [16; 17; 18; 19]. In either case, most of the former studies were conducted at post-stall angles of attack [4; 20; 21; 22] and lift characteristics were mainly discussed since interest was in the control of the separated shear layer over an airfoil. Effective parameters of PA, such as locations, burst frequencies, and others, were discussed both computationally and experimentally. Although computational studies showed that drag reduction [23] occurred in many cases, the mechanism of the drag reduction was not well discussed. From the observation of the flow fields computationally simulated by the present authors' group, pressure drag was identified to be the main source of drag reduction for the flows at the Reynolds number of order of \(10^{4}\) to \(10^{5}\), where laminar separation bubbles play an important role for the airfoil aerodynamic characteristics. Since laminar separation bubbles exist at angles of attack lower than the stall, we may expect a similar drag reduction even at pre-stall angles of attack. UAV or MAV would be considered for the application of flow control by PA at this Reynolds number range. Atmospheric wind would influence much for the flow conditions for these type of flight vehicles, and it is necessary to understand flow features and achieve high \(L/D\) for a wide range of angles of attack, and discuss flow control authority of PA. Several researchers investigate the flow at pre-stall angles of attack [24; 25; 26], but most of their work is aimed at evaluating aerodynamic characteristics, and analysis of the flow feature is not their major focus. Regarding pre-stall conditions, we have conducted two types of computational studies in the past.