## 6 Upstream Turbulence Impact  
A Q-criterion isosurface at the instant corresponding to the ejection mid-period is provided in Figure 12, for the lab-scale configuration without and with upstream turbulence. Similar flow structures are observed in both cases. However, in the presence of upstream turbulence, the hairpins are asymmetric and more bent-shaped than without upstream turbulence. This result is in agreement with the observations of [PERSON] and [PERSON] [16]. With a turbulent inlet, the hairpins lose their coherence faster and seem to remain lower in the boundary layer, implying that jets are more folded by the upstream flow. Time-averaged vertical velocity profiles are compared for the lab-scale configuration for both cases with and without upstream turbulence in Figure 13 in the jet axis (in-between jet and axial velocities are not shown for the sake of brevity). These are also compared to the experimental data. The vertical velocity (Figure 13a), which characterises the jets, is better predicted in the turbulent case; without turbulence at the inlet, the jet velocities are overpredicted. Consistent with the Q-criterion analysis, the synthetic jets are more folded in the presence of upstream turbulence. Some differences are observed for the fluctuating velocities (Figure 13b) between the numerical results and experimental data in the upstream part of the plate, before getting closer and even superposed downstream of the jets, where the simulations correctly predict the velocity profiles. Figure 14 compares the wall shear stress evolution along a period \(T\) with and without upstream turbulence for three axial positions on the plate. In order to detect general trends,  
Figure 12: Instantaneous Q-criterion isosurfaces (\(10^{6}\) s\({}^{-2}\)) along the plate, with (**right**) and without (**left**) turbulence injection at inlet. \(t=0\). Figure 13: Comparison of wall-normal velocity and associated RMS values for lab-scale numerical results with and without inlet turbulence with experimental data on jet axis at the locations \(\times\) provided in Figure 1.  
the profiles are phase-averaged over five periods. Note that an increased number of periods would be necessary to totally erase the residual turbulent fluctuations, which are still seen and are indicative of the lack of statistical convergence. Note that, in the following, the edge of the plate is assumed to be far enough from the perforations not to be impacted by the jets and is thus representative of a flat plate without disturbance. It can be noticed that, for both mid-periods, the case with turbulent inlet is characterised by a higher wall shear stress than the case without upstream turbulence. Some differences are observed between the two mid-periods. During the ejection mid-period (\(t=T/4\), Figure 14), apart from the first perforation rows, the wall shear stress in the jet wakes and between the jets are similar and characterised by important fluctuations. The jets impose the flow dynamics. On the contrary, during the suction mid-period (\(t=3T/4\), Figure 14), specific trends can be observed. Along the jet axis, the wall shear stress is not affected by the upstream turbulence and presents a similar evolution in both simulations. Between the jets, the wall shear stress evolution, for both cases, follows that of the corresponding flat plate. This implies that the flow is not driven by the synthetic jets but rather by the upstream conditions. Wall shear stress comparisons with and without upstream turbulence show that the synthetic jets drive the flow most of the time. However, upstream turbulence can become preponderant in some specific locations and at specific instants. The analysis of the temperature PDF in Figure 15 provides further understanding on how the turbulence role is important for the wall heat transfer. Since both reference and turbulent operating points are based on the same jet parameters, the same trends are found in the temperature PDF. Two main differences can, however, be noted.