The fluctuating velocity structure of open channel turbulence has a significant influence on the momentum transfer and energy dissipation. Based on the instantaneous velocity data obtained by Particle Image Velocimetry (PIV) measurements in longitudinal sections for open-channel flows over smooth and rough beds, the probability distribution of the fluctuating velocity in the inner region was discussed. The vertical distribution characteristics of the probability of turbulence events (PTE) were analyzed, and the quadrant distribution of Reynolds stress (RS) and turbulent kinetic energy (TKE), as well as the relationship between RS, TKE and PTE were studied. The results showed that after bed roughness increased, the probability distribution and organization structure of the fluctuating velocity in the inner region would change. While the probability distribution of longitudinal fluctuating velocity became sharp and presented a high narrow peak, the probability distribution of vertical fluctuating velocity gradually flattened and came close to normal distribution. Meanwhile, the strip structure of the longitudinal fluctuating velocity clearly exhibited in the inner region of the smooth bed gradually became irregular or even disappeared. The predominance of turbulence events of the 2nd quadrant and the 4th quadrant would not change with bed roughness, but the distribution characteristics of PTE would vary. When bed roughness increased, PTE of the 2nd quadrant increased in general along the total water depth, while PTE of the 4th quadrant increased only in the inner region. The bed roughness had a greater impact on the 2nd quadrant turbulence event than the 4th quadrant turbulence event. Furthermore, the predominance of the 2nd quadrant turbulence events were relatively enhanced, while the difference of PTE between the 2nd quadrant and the 4th quadrant were reduced, and the turbulence anisotropy decreased. For open channel flow with smooth bed or rough bed, the RS and TKE of the 2nd, 4th quadrant were larger than that of the 1st, 3rd quadrant, especially the values of the 2nd quadrant were at their maximum, and the quadrant TKE could account for 39.3% of the total TKE. With the increase of bed roughness, the absolute values of RS and TKE of the 2nd, 4th quadrant were increased, the increase of RS in the inner region was particularly obvious, and the increase of TKE in the inner and outer regions was close. At the same time, the change of PTE, RS and TKE in the 2nd, 4th quadrant had strong relevance.
