## 4 Results and Discussion
### VIV Response Characteristics  
As shown in Figure 6, the VIV responses of the flexible riser with buoyancy modules have two or even more vibration frequencies under a uniform flow velocity of 1.6 m/s. The frequencies of the VIV response in the CF direction for the pipe model (F01) with uniform buoyancy coverage of 25% and no helical strakes are 9.72 Hz and 3.37 Hz. The two frequencies are close to vortex-shedding frequencies of the bare pipe and buoyancy modules, which can be regarded as generated by the vortex shedding of the bare pipe and buoyancy modules. In contrast, there is only one frequency component of 3.51 Hz for the pipe (F02) with helical strakes in the CF direction, which is very close to the vortex-shedding frequency of buoyancy modules. This indicates that helical strakes suppress the generation of stable vortex shedding in the bare pipe, resulting in the absence of the bare pipe vortex-shedding frequency component in the VIV response of the riser. Similarly, compared to the pipe (F03) with buoyancy coverage of 50% and no helical strake, the pipe (F04) with helical strakes has only a buoyancy module vortex excitation frequency of 3.18 Hz in the CF direction.  
Figure 7 shows the axial distribution of the RMS value of VIV displacement calculated by the modal analysis method before and after the installation of helical strakes under the two forms of buoyancy coverage. It can be seen that the amplitude of the pipe displacement response decreases after covering helical strakes, but the decrease is limited. If the suppression efficiency is defined by the maximum reduction rate of the displacement standard deviation, for the pipe (F01) with uniform buoyancy coverage of 25%, the suppression efficiency of the VIV response is 39% in the CF direction after the installation of helical strakes. For the pipe (F03) with buoyancy coverage of 50%, the suppression efficiency of the VIV response is 42% in the CF direction after the installation of helical strakes, which is much smaller than that of the riser with full coverage of helical strakes in the literature. The reason may be that helical strakes only suppress the vortex-shedding frequency of bare pipes and have almost no influence on the vortex-shedding frequency of buoyancy modules, resulting in a large amplitude of the VIV response of the riser covering helical strakes and buoyancy modules.  
Figure 6: FFT results of VIV responses under uniform flow (1.6 m/s).  
To further investigate the suppression effect of the helical strakes on the VIV displacement, the displacement response under the vortex-shedding frequency of the buoyancy modules for the above four riser forms can be obtained by filtering. The RMS values of displacement response in the CF direction of each cross-section under buoyancy modules vortex-shedding frequency are shown in Figure 8. It can be seen that the decrease in the CF direction of the riser displacement response is not obvious after the installation of helical strakes, which indicates that helical strakes have very little influence on the vortex-shedding of the buoyancy modules, and the main effect is to suppress the VIV response of the bare pipe. The main reason is that the helical fins of strakes can control the separation of the flow. The separation point is at the tip of the stake fin, which induces a three-dimensional flow behind the cylinder breaking the vortex coherence. This is in contrast with the bare cylinder, where the separation occurs uniformly along the span, and coherent vortex shedding is generated, causing a significant VIV amplitude.