## 1 Introduction and Principle Headings  
Hydrodynamic noise is one of three major noises of underwater vehicles, and studying and controlling it are important [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]. The hydrodynamic noise is mainly caused by the velocity and pressure fluctuation in turbulent flow. Especially at medium and high velocity, hydrodynamic noise has become the main factor to affect the self-noise of sonar platforms on underwater vehicles. The study and suppression of the hydrodynamic noise on the surface of the underwater vehicle dome and towing array [11, 12, 13, 14, 15, 16] attach great importance to increase the detection range of the sonar platform and improve the signal-to-noise ratio. Traditionally, the acoustic performance of underwater vehicles is considered from linear optimization, material optimization, and structural optimization. These three traditional methods are not only difficult to implement, but also to balance the mechanical performance and the noise performance at the same time. Conversely, the superhydrophobic surface does not change the macrostructure of the sonar array platform, causes little damage to the shape of the underwater vehicles, and does not increase the wet area of the underwater vehicles. Superhydrophobic surfaces is an emerging technology that combines low surface energy chemical properties with microstructures physical properties. The discovery of superhydrophobic surfaces are inspired by the water droplet on lotus leaf. Superhydrophobicity can only be obtained if the Cassie [17] state is maintained, and this property can bring some benefits, such as drag reduction, self-cleaning and anti-fog. Microstructures on the surfaces can capture the air and transfer the liquid-solid contact to liquid-air contact, which will cause a slip velocity and change the near-wall flow regime. Scholars have studied the flow regimes changes on superhydrophobic surfaces with different parameters through experiments, simulations, and theoretical analysis. In theoretical analysis and simulation, a steady superhydrophobic surface always equivalent to free-slip or fixed slip length boundary condition. [PERSON] [18] used the free-slip hypothesis to analyze the flow regime of Stokes flow and obtained the functions of velocity distribution on superhydrophobic surfaces with different parameters. His results played a guiding role for subsequent research. Most studies on superhydrophobic surfaces are based on channel flow. The upper and lower plates in channel are set to different boundary condition to simulate the superhydrophobic surfaces. In laminar flow, the slip velocity and slip length of the superhydrophobic surface can reduce the flow resistance, and a higher proportion of the free-slip surface corresponds to a greater slip length formed by the superhydrophobic surface. As a result, the drag reduction effect of the superhydrophobic surfaces is associated with the proportion of free-slip boundary. The height of channel and the shape of microstructures also influence the drag reduction effect. The streamwise microstructures generally have better drag reduction than spanwise microstructures. The spanwise slip velocity generated by the spanwise microstructure can even increase the flow resistance. Micro-post can generate higher slip velocity than micro-grooves, but the gas-liquid interface is easily to destroyed on micro-post [19; 20; 21; 22; 23]. From the literature listed above, we concluded that the streamwise strips have a better effect on drag reduction. Hence, we chosen the streamwise strip as the object to study the noise reduction effect. In turbulent flow, the research objects on superhydrophobic surface flow are not only slip velocity and slip length, but also the vortex, Reynolds stress, and other parameters of boundary layer caused by the velocity difference between the free-slip and the no-slip surfaces.