## 1 Introduction  
The ability to manipulate a flow field with the objective to improve the efficiency and performance of airfoils is of great technological importance. Efficient flow control devices can be used to modify the laminar-turbulent transition inside the boundary layer, to prevent flow separation, to reduce drag and enhance airfoil lift. They may also be used to stabilise and mix airflow in order to reduce unsteadiness, which generates unwanted vibrations, noise and energy losses [1; 2; 3]. Both active and passive flow control devices can be used to control the flow over an airfoil. Passive techniques for flow control modify a flow without any external energy expenditure, such as geometric shaping to manipulate the pressure gradient, the use of fixed mechanical vortex generators for separation control or segmented leading edge slats. Although these devices are efficient in augmenting the lift, they create significant increases in mechanical complexity, manufacturing cost, weight and can induce a parasitic drag [4; 5]. There are several mechanisms by which active flow control techniques act; they include specifically aligned vortex generation or wall jets, and the introduction of additional momentum or energy into the flow. A localised periodic excitation close to potential separation locations can be used to impart global changes to separated flow fields, typically by flow perturbation. These perturbations can be achieved by various methods, most often by means of piezoelectric, electromagnetic and electrostatic devices, which are operated by an electromechanical driver. Compared to passive control techniques, these devices offer a significant reduction in weight, mechanical complexity and parasitic drag; however they possess limited bandwidth and are subject to mechanical failure as the driver is operated at resonance in order to meet the amplitude requirements necessary at those flight speeds [6; 7; 8]. In the course of the past decade, the use of plasma actuators for active flow control has been implemented by many researchers and has become one of the most booming realms of aerodynamics [9; 10; 11]. Dielectric barrier discharge (DBD) actuators are composed of at least two electrodes separated by a dielectric material between which a high voltage is applied, creating a plasma sheet [11; 12; 13]. Various electrode geometries are possible, and different signals can be used to excite the actuator. Flow control with plasma is appealing as the actuators used are entirely surface mounted, lack any mechanical parts and possess high bandwidth while requiring relatively low power to be actuated [9; 14]. The response time is very short, enabling real-time flow control. The effectiveness of DBD actuators has been proven for velocities up to \(Ma=0.75\), with different geometries or actuation signals showing superiority in different flow regimes [15; 16; 17; 18]. Two types of plasma generation are typically used for DBD actuators: A/C power supplies, providing a sinusoidal signal to the electrode setups, for which the dominant effects are the presence of a low-speed ionic wind by the plasma in the near-wall region, with injection of momentum in the boundary layer such as a wall-jet boundary; and secondly, nano-second pulsed power signals, that generate a localised injection of energy, a small vortex generation and a pulsing micro-shock wave [9; 11]. Typically, the actuation frequencies are expressed in terms of reduced frequency \(F_{c}^{+}\) based on chord length and freestream velocity. A preference for low frequency actuation is generally seen, with maximum flow attachment obtained in the range of \(F_{c}^{+}=1\) to \(2\) for a NACA 0015 airfoil [8; 19]. As the value of \(F_{c}^{+}\) is increased, the influence of the plasma on the flow attachment weakens. Two mechanisms of flow separation control have been reported as being effective in NS-DBD actuators. The first mechanism operates at high frequency, and is connected to the instability of the boundary layer and its turbulisation.