## 5 Results of the Sound Field of the Model  
### Distribution of the Fluctuation Pressure on the Surface of the Model  
The results of the flow field calculation are dealt with by the fast Fourier transform (FFT), and then the data of fluctuation pressure in the time domain is converted into the data in the frequency domain. The contour of the fluctuation pressure at different frequencies is shown in Figure 9. The frequency range is from 10 Hz to 2000 Hz. The boundary of the frequency is set as 500 Hz, of which the lower is considered as the low-frequency range, while the upper is the high-frequency range.  
The high fluctuation pressure at various positions on the surface of the sail hull in the low-frequency range is shown in Figure 9. In Figure 9a-c, the positions, of which the fluctuation pressure is high, coincide with what the horseshoe vortex generates, develops, and dissipates. Therefore, the high fluctuation pressure of the sail hull in the low-frequency range is induced by the horseshoe vortex. We can also see that for \(f>500\)Hz, the fluctuation pressure by the horseshoe vortex becomes smaller. A conclusion can be drawn that the flow-induced noise generated by the horseshoe vortex is mainly in the low-frequency range. The study by [PERSON] et al. has pointed out that the filled at the leading edge of the sail hull can suppress the formation of the horseshoe vortex [28]. We can infer that the method adopted by [PERSON] has little effect on the suppression of turbulent fluctuation pressure by the horseshoe vortex for \(f>500\) Hz in the model in our study. The conclusion is that if the flow control technique can suppress the flow phenomenon of the horseshoe vortex, only the flow-induced noise in the low-frequency range can be reduced.  
The boundary layer separation is that the fluid is separated from the surface of the sail hull, and the state of the laminar flow is then changed into the turbulent flow. In the process, different scales of the vortices will be generated. From the analysis of the last paragraph, the large-scale vortices make  
Figure 9: Distribution of the fluctuation pressure on the surface of the model at different frequencies: (**a**) \(f=50\) Hz; (**b**) \(f=200\) Hz; (**c**) \(f=400\) Hz; (**d**) \(f=600\) Hz; (**e**) \(f=800\) Hz; (**f**) \(f=1000\) Hz; (**g**) \(f=1600\) Hz; and (**h**) \(f=2000\) Hz. The left color bar shows the magnitude of the fluctuation pressure.  
the model radiate the low-frequency noise, while the small-scale vortices generate the high-frequency noise. Therefore, the noise generated by the boundary layer separation is in the whole frequency range. For \(f\) > 500 Hz, the sound radiation from the sail hull is considered to be induced by the excitation of the boundary layer separation. Therefore, if the flow control device is aimed to suppress the large-scale vortices, the flow-induced noise in the low-frequency can be reduced, while if the flow control device is aimed to inhibit the small-scale vortices, then the flow-induced noise in the high-frequency can be decreased.  
The vortices that fall off from the trailing edge of the sail hull can make the model radiate the noise of the single frequency, because of the quasi-periodical tail vortex shedding. The frequency of the tail vortex shedding is:  
\[f=\frac{S_{t}\cdot U}{l}, \tag{24}\]  
where \(S_{t}\) is the Strouhal number, \(U\) is the incoming velocity, and \(l\) is the feature length of the model. Based on the parameters of the model, the frequency of the tail vortex shedding is 595 Hz. Therefore, the high turbulent fluctuation pressure on the surface of the sail hull in Figure 9d is considered to be induced by the model under the excitation of the tail vortex shedding. The noise of the model at the frequency of 600 Hz is also called the tail vortex shedding noise. The analysis is consistent with [PERSON]'s study in the aerodynamic field [29], who has made the structure of the sawtooth significantly reduce the tone noise by the excitation of the tail vortex shedding.