## 3 Discussion  
### Turbulent Structures Changes on Superhydrophobic Surfaces  
The hydrophones are arranged in the centerline of flow region where flow is stable to precisely collect sound pressure. Otherwise, the data of hydrophones are averaged. On consideration of the sampling theorem, the CFL condition, and the ram of computer, we set the frequency range to 100-30 kHz and the resolution to 100 Hz. The grid size of sound domain is one-sixth wavelength. First, we compared the pressure changes of the superhydrophobic surface with alternating boundary conditions, as shown in Figures 8 and 9. We fixed the fraction of the free-slip boundary as GF is 0.5 and compared the pressure distribution when the strip numbers are 1, 2, 4 and 8. In general, the pressure fluctuation of the no-slip surface is significantly higher than the superhydrophobic surface with strips at different numbers. The Figure 9 shows that the root mean square error of pressure at different strip number and GF. Similar to the distribution of boundary conditions, the pressure also exhibits alternating properties. When the number of strips is 2, a large range of low-pressure fluctuation areas are concentrated on the free-slip surface and multiple continuous high-pressure areas and low-pressure areas exist at the free-slip strips. Consequently, the pressure RMSE at \(Strip\ number=2\) has the largest value than others. As the number of strips increases, the frequent alternation of the free-slip and no-slip boundary results in an interactive influence. As a result, the fluctuating pressure is enhanced, and the range of continuous stable pressure areas decrease. When the number of strips is 8, the fluctuating pressure on superhydrophobic surface is close to the no-slip surface, and the noise reduction effect has been weakened. The vorticity contours are shown in Figure 10, to further study the influence of flow regime changes on flow noise. According to vortex sound theory, the vortex is the voice of the fluid, we compared the vorticity of different strip numbers at \(GF=0.5\). The vorticity contours of no-slip boundary channel is shown in Figure 10a. The vorticity is large at the overall flow field, especially at the near-wall region. However, the vorticity at free-slip boundary is 0, and the channel with free-slip boundary has a lower vorticity level. When the strip number is small, the vorticity distribution is more centralized. A clear boundary between the zero vorticity and the large vorticity is observed. The free-slip boundary and no-slip boundary have less mutual influence. The flow noise should have a lower level because of the large-scale lower vorticity distribution. However, when the strip number becomes large, the space between the free-slip and no-slip boundary becomes narrow. The interactive influence of free-slip and no-slip is obvious, and the lower vorticity part nearly disappears. Consequently, the flow noise level can be higher when the strip number is large. Figure 7: Boundary condition of sound simulation domain and hydrophone array. Note that the streamlines of velocity on \(YZ=3.5\delta\) cutplane are shown in Figure 11, we can draw the same conclusion. The channel with no-slip bottom boundary generates more lateral vortices. At the center of the flow field, the larger vortices can be found, which will generate higher low-frequency noise. Otherwise, small vortices are generated near the wall and increases the high-frequency components. As a result, the no-slip channel has a higher overall noise level. However, the number of lateral large vortices on the superhydrophobic surfaces with \(Strip\ number=2\) is significantly reduced, while the number of small vortices near the wall does not increase significantly. Therefore, the flow noise level must be lower. As the number of strips increases, more vortices will be generated with a size close to the strip width on the bottom and significantly affect the flow noise at some certain frequencies. Figure 8: Contours of pressure distribution at the bottom wall of channel. (**a**) no-slip.