# Pressure Fluctuation and Flow-Induced Noise of the Fin and Rudder in a Water Tunnel
## 1 Introduction  
Ocean noise has increased sharply in recent years due to the increase in human oceanic activities such as shipping, seismic exploration, and scientific investigation [1]. The underwater noise radiated by ships propagates as sound pressure waves in the water, affecting marine organisms, ecosystems, and the environment [2]. It is necessary to understand and reduce the radiated noise produced by ships [3, 4]. In order to reduce underwater radiated noise generated by commercial shipping, the International Maritime Organization (IMO) has issued revised guidelines for reducing underwater radiated noise produced via shipping to limit its adverse impacts on marine life [5]. A rudder serves as the primary component for controlling the direction of ships and underwater vehicles, but its turbulence induces hydrodynamic noise that radiates directly into the ocean. As flow velocity increases, this noise rapidly increases and cannot be disregarded [6]. Therefore, comprehending the mechanisms behind hydrodynamic noise generation from rudders is crucial in reducing its occurrence. The hydrodynamic and noise characteristics of underwater rudders have been discussed by many scholars under different application scenarios. [PERSON] et al. [7] conducted tests on a hydrofoil in a water tunnel facility, confirming the effectiveness of employing leading-edge isolation technology to reduce hydrofoil vibration and noise, resulting in anoise reduction of 5 to 10 dB. [PERSON] et al. [8] carried out an experimental study on a transient flow field around a propeller-rudder system in a cavitation tunnel and discussed the interaction between the propeller's wake flow and the rudder. In a wind tunnel, [PERSON] et al. [9] built a submarine model with a rudder installed behind the DARPA SUBOFF and tested the effects of the rudder on its wake. [PERSON] et al. [10] used LES to study the flow field of a two-dimensional flap rudder and found that there were almost no eddies generated in the gap between the flap and the rudder when the angle of the flap was zero. [PERSON] et al. [11] predicted the flow-induced noise of an underwater vehicle without appendages, an underwater vehicle with a sail, and underwater vehicles with different types of rudders (cross-type, X-type, and T-type) and compared the radiated noise and directivity of these different objects. [PERSON] et al. [12] adopted a corrected reverberation-measuring method and conducted experimental research on flow-induced noise in a submerged wing-shaped cavity in a gravitational water tunnel. Based on the experimental and simulation-derived results, they summarized that the sound power of a wing-shaped cavity is proportional to five to six times the power of the flow velocity. [PERSON] et al. [13] utilized the FW-H method to investigate the flow noise generated by an oscillating hydrofoil and explored the influence of the Reynolds number, reduced frequency, and the Strouhal number on the sound pressure level. The results revealed a dipole-like pattern of sound at specific frequencies, influenced by the hydrodynamic coefficient, while the directivity of dipole axes was affected by the reduced frequency. Although the influence of the rudder on noise radiation was found to be different under different working conditions, research on the hydrodynamic and acoustic performance of the rudder itself will help us to design a quiet rudder. In terms of numerical simulation, [PERSON] et al. [14] utilized Large Eddy Simulation (LES) to predict and analyze the flow-induced noise of an airfoil at a low angle of attack and obtained sound pressure spectrum results at far-field measuring points and directivity results regarding the OSPL. [PERSON] et al. [15] applied two hybrid methods, LES with acoustic analogy theory and LES with vortex sound theory, to predict the flow-induced noise of an airfoil. The two numerical methods based on LES both yielded stable results, consistent with the experimental data. By combining the LES and boundary element methods, [PERSON] et al.