## 4 Results and Discussion
### Flow Control of Plasma Actuators in Flowing Air
The reason for these phenomena may be that the actuators are placed behind the flow separation point so that the flow separation is completely caused by the architectural shape (i.e., the leading-edge, sharp corner of the roof). Figure 13: Contours of the fluctuating pressure coefficient and its change rate on the whole roof: (**a**) no actuation; (**b,c**) case A; (**d,e**) case B; (**f,g**) case C.  
The RMS value of the velocity may be regarded as the fluctuating velocity. In the recirculation zone, it is primarily produced by the shedding vortices as a consequence of the flow separation at the front edge of a low-rise building. The region of the maximum fluctuating velocity is located in the near wake behind the building model, as shown in Figure 15. Obviously, the fluctuating velocity area of over 2.7 m/s for each case is lower than that of the no actuation situation. This shows that the active actuators can manipulate the vortex shedding process in the wake. It is remarkable that the area of the fluctuating velocity greater than 3.1 m/s disappears completely in case A. This decline means that case A with the actuation is the most capable of mitigating the strength and size of the wake vortices. Figure 14: Contours of mean \(x\)-velocity component: (**a**) no actuation; (**b**) case A; (**c**) case B; (**d**) case C.  
Figure 15: RMS velocity contours: (**a**) no actuation; (**b**) case A; (**c**) case B; (**d**) case C.  
To fully demonstrate the mechanism of plasma flow control, the no actuation situation and case A are selected for further comparison and analysis. For the flow control of the building structure, the spanwise vortex structure can be identified by the spanwise vorticity (i.e., the \(y\)-vorticity component), and the streamwise vortex structure can be identified by the streamwise vorticity (i.e., the \(x\)-vorticity component) [30]. Figure 16 shows the temporal evolution of the instantaneous \(y\)-vorticity component for case A and the no actuation situation. It can be observed that under the action of the wall jet, many small-scale spanwise vortices continue to appear on the roof. Figure 17 shows the temporal evolution of the instantaneous \(x\)-vorticity component for case A and the no actuation situation. When there is no actuation, almost all pairs of streamwise shedding vortices exist in the recirculation zone. It can also be noted at the same time that the strength and size of these streamwise vortices are significantly reduced after the actuators are ignited. These results indicate that the active actuators can result in the formation of small-scale spanwise vortices so as to restrain the strength and size of streamwise shedding vortices in the recirculation zone. Figure 10:0 Evolution of instantaneous \(y\)-vorticity component with the time \(t\): (**a,b**) \(t=18\) s; (**c,d**) \(t=18.045\) s; (**e,f**) \(t=18.09\) s.  
The skin friction coefficient \(C_{f}\) (\(=\tau_{w}/0.5\rho V_{h}{}^{2}\)) can be calculated by the wall shear stress \(\tau_{w}\)[31]. Figure 18 illustrates the contours of mean skin friction coefficients on the building surfaces for all cases. The mean \(C_{f}\) distribution of each case on the windward and lateral walls is almost the same as that of the no actuation situation, indicating that the active actuators have no influence on the skin friction coefficient of the wall. Compared with the no actuation situation, the mean \(C_{f}\) of all cases on the roof surface is increased obviously. Each local roof area with the increase of mean \(C_{f}\) is located just below the plasma active region. These results indicate that the active actuators can increase the velocity gradient on the roof surface. Figure 10:1 Evolution of instantaneous \(x\)-vorticity component with the time \(t\): (**a**,**b**) \(t\) = 18 s; (**c**,**d**) \(t\) = 18.045 s; (**e**,**f**) \(t\) = 18.09 s.