## 1 Introduction  
There is an increased drive among industries and policy makers to reduce the amount of carbon dioxide emissions using renewable energy sources and to improve the efficiency of current energy conversion processes. Evidence of this can be seen in the Clean Sky 2 program, an innovation program bringing together the European aviation industry and academia, to achieve 50% reduction in fuel consumption and carbon dioxide emissions by 2020 [1]. Renewable energy sources are increasingly coming to the fore as a means to cut carbon emissions; tidal energy could theoretically provide 1 TW of energy from the more accessible coastal regions [2]. Synthetic jet actuators can help provide potential gains, some marginal and some significant, in improving the efficiencies in both these areas. The outcomes of the present research may add to the progression and development of active flow control through the characterisation of the use of synthetic jet actuators for a cylinder in cross flow. In recent years, synthetic jet actuators have proven to be useful devices for a wide range of flow control applications [3]. Synthetic jets have been implemented to enhance heat transfer through turbulent mixing [4] as well as being utilised to modify the boundary layer to notably increase lift and decrease drag forces experienced by a body [5]. Studies using NACA0015 aerofoils have achieved a 100% increase in lift and 26.5% decrease in the corresponding drag [6]. Other works have shown increases of 80% in lift as well as increasing the stall angle from 12\({}^{\circ}\) to 18\({}^{\circ}\)[7]. These changes in the performance of an aerofoil have significant implications on both the payload an aircraft can carry as well as its fuel economy. These optimum operating points are often characterised by a dimensionless actuation frequency \(F^{+}\) (Equation (1)):  
\[F^{+}=\frac{f_{a}L}{U_{\infty}} \tag{1}\]where \(f_{a}\) is the jet actuation frequency, \(L\) is a characteristic length scale (e.g., chord length) and \(U_{\infty}\) is the freestream velocity. Synthetic jet actuators are zero net mass flux devices that can alter lift and drag forces by modifying the boundary layer and wake for a body in cross-flow. Boundary layer modification by a synthetic jet emanating from a surface is achieved through a propagating train of vortices. These vortices are created by an oscillating diaphragm within a cavity inside the body [8; 9]. As the fluid passes over the sharp edge of the orifice, the shear flow causes the fluid to roll up into a vortex [10]. If the diaphragm deflection amplitude is sufficiently large, the vortex separates from the orifice. On separation, the vortex ring moves with a near constant velocity in a direction perpendicular to its orifice exit plane (at least in quiescent fluid) as a result of the hydrodynamic impulse and thereby momentum is imparted on the surrounding fluid [11; 12]. Due to the repeated oscillation of the diaphragm, vortices are ejected periodically from the orifice. Thus, a jet is'synthesized' from the surrounding fluid, which imparts momentum to the boundary layer without adding net mass flux [10]. The physical behaviour of a synthetic jet actuator and its optimal design criteria can be described by lumped element or reduced-order models [4; 13; 14], using a combination of analytical modelling and empirical coefficients which can be determined through calibration [4]. In cross-flow, the synthetic jet alters the viscous sublayer passing over a body. This alteration modifies the location of the separation point on the surface of the body. By altering the separation point as well as the characteristics of the downstream wake, synthetic jet actuation allows for the lift and drag forces experienced by the object to be altered [10; 15; 16; 17; 18].