## 4 Reynolds Number Effect on VIV Characteristics and the Underlying Mechanism
### Time-Frequency Characteristics of Dynamic Aerodynamic Forces
#### 4.2.2 RMS Values of the Wind Pressure Coefficients  
Figure 10 shows the distribution characteristics of the RMS values of the wind pressure coefficients on the surface of the main beam in the free vibration test.  
As shown in Figure 10a, the RMS values on the upper surface in the free vibration tests exhibit significant variations across different Reynolds numbers. When \(Re=3.2\times 10^{4}\) and \(Re=4.7\times 10^{4}\), the RMS values on the upper surface exhibit considerable changes, reaching their maxima near the downstream railings. As the Reynolds number increases, \(C_{\rm p,rms}\) decreases. Specifically, from \(Re=3.2\times 10^{4}\) to \(Re=4.7\times 10^{4}\), \(C_{\rm p,rms}\) decreases by a maximum of 0.07, approximately 60%. From \(Re=4.7\times 10^{4}\) to \(Re=7.1\times 10^{4}\), \(C_{\rm p,rms}\) decreases by a maximum of 0.13, approximately 65%, and its spatial distribution characteristics change. When \(Re=8.3\times 10^{4}\), the RMS values are similar to those at \(Re=7.1\times 10^{4}\), with no significant change and relatively small values, remaining below 0.05.  
As shown in Figure 10b, the distribution characteristics of \(C_{\rm p,rms}\) on the lower surface across different Reynolds numbers are similar, but the values differ. Near \(D_{\rm d}=0.03\), there is a local maximum in \(C_{\rm p,rms}\). As the dimensionless distance increases, \(C_{\rm p,rms}\) becomes relatively stable. As the Reynolds number increases, \(C_{\rm p,rms}\) on the lower surface decreases. From \(Re=3.2\times 10^{4}\) to \(Re=8.3\times 10^{4}\), at \(D_{\rm d}=0.03\), \(C_{\rm p,rms}\) decreases from 0.31 to 0.04, a decrease of 0.27 or approximately 87%. At \(D_{\rm d}=0.48\), \(C_{\rm p,rms}\) decreases from 0.07 to 0.02, a reduction of 0.05 or approximately 71%.  
Overall, with increasing Reynolds number, the RMS values of the wind pressure coefficients on both the upper and lower surfaces decrease, and their spatial distribution characteristics change. Combined with the variation in VIV with the Reynolds number, the  
Figure 10: Distribution characteristics of the RMS values of the wind pressure coefficients at different Reynolds numbers. (**a**) Upper surface. (**b**) Lower surface.  
Figure 9: Distribution characteristics of the mean values of the wind pressure coefficients at different Reynolds numbers. (**a**) Upper surface. (**b**) Lower surface.  
reduction in surface RMS values may be one of the reasons for the weakening of VIV. A comparison between the static and free vibration tests reveals that the RMS distributions differ, with the static test yielding much smaller values than the dynamic tests do. Both static and dynamic tests show a decreasing trend in the RMS values with increasing Reynolds numbers, but the specific variations differ.  
In summary, in the free vibration tests, the mean values of the wind pressure coefficients on the main beam surface exhibit a slight Reynolds number effect in certain regions, whereas the RMS values show a significant Reynolds number effect, decreasing with increasing Reynolds numbers, and their distribution characteristics change. The motion state of the main beam has little effect on the mean values and their Reynolds number effects, whereas it has a noticeable effect on the RMS values and their Reynolds number effects. The above studies reveal the influences of the Reynolds number and the motion state on the mean and RMS values of the wind pressure coefficients, which provides a reference for future related research.