## 1 Introduction  
A common definition of boundary layer flow control was given by [PERSON] [1]: \"Boundary layer control includes any mechanism or process through which the boundary layer of a fluid flow is caused to behave differently than it normally would were the flow developing naturally along a smooth straight surface\". Due to the increase of computational resources and the development of sensor and actuator technology, the numerical and experimental implementation of advanced flow actuation has accelerated rapidly during the past 15 years [2]. The ability to control unwanted fluid flow occurrences is motivated by the desire to improve the aerodynamic performance of air vehicles. For decades, the aerospace industry has actively developed technologies that can eliminate, or at least mitigate, unwanted boundary layer separation [3; 4; 5]. In fluid dynamics, separated flow may cause an increase in aerodynamic drag, induce mechanical vibration, and decrease lift. These flow features contribute to poor aerodynamic characteristics and structural failures. Thus, by providing effective control and separation mitigation, we can design optimized high-performing air vehicles. Some common boundary layer control devices are: vortex generators, moving surfaces, dimpled surface textures, and serrated trailing edge geometries. These devices are regarded as \"passive\" due to their continuous perturbation of the baseline fluid flow. The other method of flow control is typically described as \"active\". This option enables variable actuator operation and is desirable for unpredictable flow conditions. Common examples of active flow control techniques are: plasma actuators, mechanical suction and blowing, and piezo electric driven cavities. Plasma-actuator based flow control has been shown to provide a drag reduction and lift augmentation through the redistribution of boundary layer momentum from high-to-low regions [6]. These active flow control devices have become increasingly popular due to their ability to adapt to atmospheric conditions, low maintenance costs, and minimal parasitic drag penalty. A plasma can be defined as follows: \"A plasma is a quasi-neutral gas of charged and neutral particles which exhibits collective behavior\" [7]. There are several common types of plasma actuators used for aerodynamic flow control: glow discharges, DBDs, and magnetically-accelerated surface discharges are some of the most popular. DBDs are one of the commonly used actuators for active flow control of low speed applications. [PERSON] first introduced this plasma actuator in 1857 for ozone generation [8; 9]. A schematic of a typical DBD plasma actuator is shown in Figure 1.  
A DBD plasma actuator is comprised of two asymmetric electrodes and a dielectric material, i.e., glass, Kapton, or Teflon. A dielectric material is utilized to insulate one electrode, while the other is exposed to the ambient conditions. The electrode terminals are connected to a direct current (DC) or alternating current (AC) voltage power source. A DC power source is commonly used for spark discharge plasma actuators, whereas an AC power source is appropriate for DBD plasma actuators, which are frequently called quiet release actuators [8]. The AC voltage applied to DBD actuators varies from 5 kV to 20 kV with a frequency range of 3-15 kHz [10]. When a high voltage and frequency is applied, the region exposed to the open electrode ionizes because of the drift of electrons from one electrode to another (i.e., cathode to anode). The chemical reaction for this process is:  
\[A+e^{-}=A^{+}+2e^{-} \tag{1}\]  
This ionized gas (plasma) moves towards the covered electrode. The ions produce a body force due to the momentum transfer of the flow close to the wall surface. This causes a suction effect above the uncovered electrode and works similarly to a wall jet. The plasma development is strongest in the area close to the electrodes.