## 4 Conclusions  
This study employs Particle Image Velocimetry (PIV) to investigate the turbulent boundary layer over smooth, streamwise riblet, and convergent-divergent riblet wall surfaces. The results demonstrate that riblet walls with different yaw angles significantly influence the statistical properties, streak structures, and burst events within the turbulent boundary layer, thereby affecting the generation of wall frictional resistance. Compared to the statistical properties of the turbulent boundary layer on a smooth wall, the divergent riblet wall has the opposite effect on the turbulent boundary layer compared to the convergent riblet wall, while the streamwise riblet wall has a similar effect on the divergent riblet wall but with a weaker impact. The divergent and streamwise riblet walls cause the velocity profile curve in the logarithmic law region to shift upwards, resulting in a decrease in boundary layer thickness and friction velocity. The overall turbulence intensity and Reynolds shear stress within the boundary layer are reduced, indicating that these two types of riblet walls have good drag reduction characteristics. The addition of particles can lead to an increase in boundary layer thickness, a reduction in wall friction resistance, and a decrease in overall turbulence intensity and Reynolds shear stress within the logarithmic law region. However, it can also have a certain enhancing  
Figure 14: Contour cloud map of Reynolds shear stress distribution during ejection events: (a) ejection event in the clear water flow field at a height of \(y^{+}=90\); (b) ejection event in the two-phase flow field at a height of \(y^{+}=90\); (c) ejection event in the clear water flow field at a height of \(y^{+}=30.5\); (d) ejection event in the two-phase flow field at a height of \(y^{+}=30.5\). effect on the overall turbulence intensity and Reynolds shear stress in the buffer layer and part of the wake region. By performing a proper orthogonal decomposition on the velocity field of the \(x\)-\(z\) plane, the large-scale streak structures that dominate the near-wall region were obtained. Compared to the smooth wall, drag reduction riblet walls reduce the energy content ratio of the streak structures and advance the modal order at which smaller-scale structures appear. In contrast, drag-increasing riblet wall have the opposite effect. After the addition of particles, a fragmentation effect occurs on the streak structures, reducing the energy content ratio of the first three modal orders. Subsequently, the spacing of the streak structures was quantitatively analyzed through correlation function analysis. At the same wall-normal position, drag-reduction riblet walls widen the spacing of the streak structures, while divergent riblet wall enhance the spanwise motion of the streak structures. Particles, while fragmenting the streak structures, also reduce the spanwise spacing of the streak structures. The statistical results are well in line with the morphological changes in the streak structures in the low-order modes. The new quadrant division method was used to extract burst events near the normal heights of \(y^{+}=90\) and \(fy^{+}=30.5\). The results show that, in the clear water flow field at both heights, the drag reduction riblet walls have a minimal impact on the fluctuating velocity components of burst events but reduce the number of ejection events, decreasing their contribution to Reynolds shear stress. In contrast, drag-increasing riblet walls enhance the aforementioned effects. The addition of particles effectively suppresses the fluctuating velocity components of burst events and intensifies the role of drag-reduction riblet walls, further reducing the number of ejection events and the [PERSON] shear stress they produce. Although the intensity of burst events at the normal height of \(y^{+}=30.5\) is weaker than at \(y^{+}=90\), their contribution to [PERSON] shear stress is not significantly reduced. Conceptualization, Y.Z., J.S. and N.J.; methodology, Y.Z., J.N. and J.Y. ; software, Y.Z., J.N.