# Drag Reduction in Compressible Channel Turbulence with Periodic Interval Blowing and Suction
## 3 Results and Discussions
### Reynolds Stress  
The Reynolds normal stress (RNS) \(\langle u^{\prime+}u^{\prime+}\rangle\) and the Reynolds shear stress (RSS) \(\langle u^{\prime+}v^{\prime+}\rangle\) can reflect the turbulence intensity. Figure 7 presents the Reynolds normal stress on the blowing/suction side at various Mach numbers. The Reynolds stress on the blowing/suction side is normalized by the spatially averaged wall friction velocity on the bottom/top wall, respectively. Comparing Figure 7a,c, the RNS peak on the blowing side in C2-C5 is higher than the basic flow, which is consistent with the aforementioned literature [10]. Furthermore, the RNS peak is at \(y^{+}\approx 15\) for \(Ma=0.8\) and \(y^{+}\approx 20\) for \(Ma=1.5\). The wall-normal height of the RNS peak increases with the blowing intensity, but the distinction is not readily apparent at the same Mach number. The RNS peak in the blowing region is lower than that in the uncontrolled region, and this discrepancy also expands with the blowing intensity. In Figure 7a, the RNS peak is the highest in C2 at \(Ma=0.8\), followed by C4, C3, and C5. This reveals that the spatially averaged RNS peak on the bottom wall declines as the \(\alpha\) decreases generally, but it rebounds when \(\alpha=1/3\). In Figure 7c, the relationship between the RNS peak and \(\alpha\) becomes unclear at \(Ma=1.5\). Figure 7: Spatially averaged Reynolds normal stress in different regions. The legend description is the same as Figure 6.  
On the contrary, the spatially averaged RNS peak on the suction side in C2\(\sim\)C5 is lower than the basic flow, as shown in Figure 6(b),d. The spatially averaged RNS peak on the suction side is located at \(y^{+}\approx 17\) for \(Ma=0.8\) and \(y^{+}\approx 22\) for \(Ma=1.5\), which is slightly higher than the blowing side. In contrast to the blowing side, the wall-normal height of the RNS peak decreases with the suction intensity. Additionally, the spatially averaged RNS peak in the suction region exceeds that in the uncontrolled region. In Figure 6(b), the RNS peak diminishes with the increasing \(\alpha\) at \(Ma=0.8\), but it recovers and even exceeds that in C2 when \(\alpha=1/5\). In Figure 6(d), the spatially averaged RNS peak on the suction side in C10 is still the highest, but the spatially averaged RNS peak in the suction region in C10 is inferior to that in C8. The suction intensity in C10 is significantly violent, resulting in a pronounced diminishing influence on the RNS peak. Figure 8 depicts the spatially averaged Reynolds shear stress (RSS) on the blowing/suction side at various Mach numbers. Given that the RSS in the basic flow and on the blowing side of the controlled cases is negative, \(-\langle u^{\prime+}v^{\prime+}\rangle\) is designated as the ordinate variable in Figure 7(a),c. The RSS peak is at \(y^{+}\approx 37\) and \(y^{+}\approx 48\) for \(Ma=0.8\) and \(1.5\) on the blowing side, while \(y^{+}\approx 35\) and \(y^{+}\approx 44\) for \(Ma=0.8\) and \(1.5\) on the suction side, respectively. In Figure 7(a),c, the spatially averaged RSS peak on the bottom wall in C2\(\sim\)C5 and C7\(\sim\)C10 exceeds that of the basic flow. However, the spatially averaged RSS peak value within the blowing region is lower than that in the uncontrolled region. As the blowing intensity increases, the spatially averaged RSS peak in the blowing region rapidly declines, and the spatially averaged RSS peak on the wall also diminishes. In Figure 7(b),d, the spatially averaged RSS peak on the top wall increases with the suction intensity in general. However, it is found that the RSS peak falls back in C5. Figure 8: Spatially averaged Reynolds shear stress in different regions. The legend description is the same as Figure 6.  
The results indicate that, with an increase in blowing intensity, the peak position of the Reynolds stress shifts upward. This suggests that the primary energy-containing structures in the buffer layer, including low-speed streaks and quasi-streamwise vortices (QSV), are influenced by blowing control and migrate away from the wall.