## 3 Results and Discussion
Figure 5:0 Effect of time and spatially averaged turbulence intensity at the rear of the cylinder on \(C_{D}\) as a function of \(St_{o}:\) (**a**) Change in turbulence intensity and \(C_{D}\) with \(St_{o}\); (**b**) Change in \(C_{D}\) with turbulence intensity. Exactly how these mechanisms affect the surface pressure coefficient \(C_{p}\) can be seen more readily upon closer inspection of Figures 13 and 14. Since the stagnation pressure remains unchanged across the range of actuation frequencies, a direct comparison of \(C_{p}\) plots can be carried out. Comparing two cases of jet Stokes number \(St_{o}\) = 2.43 and 4.86 (Figure 14), the corresponding increase in turbulence intensity \(I\) from 9.4% to 10.2% appears to transform the pressure distribution, decreasing the magnitude of all maxima and minima of \(C_{p}\) (Figure 14). It appears that the bulk of the drag reduction is due to the reduction in the pressure magnitude between \(\frac{\pi}{2}\) and \(\frac{3\pi}{2}\) and hence the reduction in the positive force in the \(x\) direction (Equation (7)). It is interesting to note the asymmetry when comparing the \(St_{o}\) = 2.43 case (Figure 14a) with the \(St_{o}\) = 4.86 case (Figure 14b). The asymmetry of the time-averaged \(C_{p}\) results offers little correlation between the degree of asymmetry and the drag reduction; only the decrease in the pressure magnitude accounts for this reduction. The downstream flow domain was observed from the lee of the cylinder at a distance ranging from zero to 16 diameters (\(16D\)) downstream. For the spatial averaging aspect, the properties of the flow domain were recorded along a series of lines extending \(\pm\)3.5\(D\) in the \(y\) direction and spaced \(2D\) apart from \(0D\) to \(16D\) from the lee of the cylinder. As previously mentioned, the turbulence intensity at the freestream velocity inlet was fixed at 5%. How the turbulence intensity downstream of the cylinder varies with actuation frequency can provide valuable information for wind or tidal turbine arrays, particularly if the jet operating conditions that yield the minimum drag coefficient \(C_{D}\) and RMS lift coefficient \(C_{L}^{\prime}\) values were to have a negative effect at far field downstream locations, e.g. in the form of increased turbulence intensity. This turns out not to be the case, as described below. Across all cases modelled, unactuated or actuated, regardless of frequency, at no point in the flow domain does the averaged turbulence intensity return to 5%. The minimum turbulence intensity of 6.7% occurs at \(2D\) downstream of the cylinder. The near-wall turbulence intensity in the lee of the cylinder ranges from 10.2% (for \(St_{o}\) = 4.68) to 8.8% (for \(St_{o}\)= 4.21). A common trend for all cases in Figure 15 is that the turbulence intensity decreases in the near-wake, over the first distance of \(2D\). Beyond \(2D\) downstream, the turbulence intensity increases with distance. The peak turbulence intensity (for the unactuated case and actuated cases with \(St_{o}\) = 2.43, 3.44, 4.21 and 6.43) ranges from 11.9% to 13.0% at a downstream distance of \(14D\) from the cylinder. After this point, there is a small decrease before the end of the flow domain is reached. The cases for \(St_{o}\) = 4.86, 5.43 and 5.95 have not yet reached a maximum turbulence intensity at the end of the flow domain. The flow domain would  
Figure 5:1 Alteration of pressure gradient across the jet orifice \(\frac{dP}{d\theta}\) and the corresponding near-wake turbulence intensity \(I\) as a function of \(St_{o}\): (**a**) Change in turbulence intensity and \(\frac{dP}{d\theta}\) with \(St_{o}\); (**b**) Change in turbulence intensity with \(\frac{dP}{d\theta}\).