## 1 Introduction and Principle Headings
In the study of flow regime on superhydrophobic surfaces, the turbulent flow on superhydrophobic surfaces have obvious changes compared with ordinary smooth surfaces, and the influence of these changes on hydrodynamic noise is still unclear. In turbulent flow, [PERSON] and [PERSON] [24] studied the influence of streamwise and spanwise slip boundary conditions on turbulent flow through direct numerical simulation. Their results proved that streamwise slip length can effectively weaken the turbulence intensity and vortex, while the spanwise slip length increases the flow resistance. Thereafter, the flow under different microstructures' type, size, spacing, and air-water contact area fraction on superhydrophobic surfaces under different Reynolds numbers have been studied. They found that the increase in the microstructure spacing, the decrease in the proportion of no-slip surface, and the change in the number of microstructures cause significant changes in the Reynolds stress distribution and significantly weaken the flow resistance. Otherwise, micro-posts with large spacing have better drag reduction effects than micro-riblets, but the turbulent structures have a slight difference. Angular microstructures will reduce the secondary flow and turbulent sweeping up and down movement. As the increase in Reynolds number reduces the drag reduction effect, the effective slip length of the wall still increases [22; 25; 26; 27]. [PERSON] [28] verified that constant pressure gradient (CPG) in the study of the turbulent structure on superhydrophobic surfaces is more profit than constant flow rate (CFR). They analyzed the flow regime changes on superhydrophobic surfaces from different turbulent parameters, and proposed the generation and distribution of secondary flow on superhydrophobic surfaces. [PERSON] [29] studied on a larger size scale of microstructure and selected microstructures of micro-posts and micro-ridges. The results showed that the influence of size on the micro-posts is more obvious than that on micro-ridges. Friction Reynolds number changes slightly affect the flow structure, while the size of microstructures and Weber number are important factors of the turbulent structure. [PERSON] [30] separatedthe influence of the slip length and the surface topography on superhydrophobic surfaces, and proved that the turbulent structure changes are mainly affected by the surface topography. [PERSON] [31; 32] simulated and analyzed the flow of superhydrophobic surfaces under different gas-liquid contact surface angles at different Reynolds numbers. [PERSON] [33] compared channel flow and pipe flow under similar boundary conditions. They found that the lateral slip in the superhydrophobic pipe is relatively large and certain vorticities has been formed. Furtherly, the vorticities will generate secondary flow and weaken the energy transport of convective vortices. [PERSON] [34] used equivalent boundary conditions to analyze the vorticities, Reynolds stress, and the reasons for velocity increment in the pipeline. Therefore, in the analysis of flow noise, the secondary flow and the parameter changes of microstructures probably play an important role in the analysis of flow noise. In addition to numerical simulations, many experimental studies are conducted on the flow regimes of superhydrophobic surfaces under turbulent flow. [PERSON] [35] first studied the flow on superhydrophobic surfaces with microstructures. The results are consistent with [PERSON] and [PERSON]'s DNS results and the theoretical analysis of [PERSON] [36]. Therefore, the flow changes caused by the increase in depth and space improved the drag reduction effect of the superhydrophobic surface under a given Reynolds number. Otherwise, when the thickness of the viscous bottom layer is close to microstructures, the drag reduction effect will be significantly increased. These results verify the possibility of using superhydrophobic surfaces in underwater vehicle.