## 1 Introduction  
China has a long and winding coastline dotted with numerous islands along the waterway, creating a complex navigational environment. Due to the effects of tides, vortex fields are often induced near reefs and islands. The spatial scale of vortex fields near reefs ranges from 0.1 to 10 km [1], with time lasting from several hours to days [2]. Despite its small temporal and spatial scales, ships passing through vortex fields are sometimes threatened by lateral thrust, eccentric lifting forces, and bow-stern unbalanced force couples [3]. These adverse impacts can impair the maneuverability of navigating ships, and may even cause small ships to lose control or capsize. For ships in the channels in reef sea areas, the risk and complexity of navigation increase significantly due to the presence of vortices. Therefore, for safety reasons, it is necessary to conduct monitoring studies on vortex fields in these channels to provide scientific guidance and decision-making support. Acoustic waves, characterized by low attenuation in water, are suitable for monitoring vortex fields in channels. When propagating through vortex fields, acoustic waves couple with the vortex fields, and the resulting signals are referred to as vortex acoustic signals. The phase characteristics of vortex acoustic signals can aid in the determination of the presence of vortices, forming a vortex field monitoring method based on the phase characteristics of acoustic signals. This method is cost-effective and available for real-time dynamic monitoring. For decades, extensive research has been conducted on acoustic-vortex coupling through numerical simulations. [PERSON] et al. [4] compared the radial velocity distributions and vortex speed profiles of Rankine vortices and Burgers vortices by simulating the acoustic scattering phenomena. [PERSON] et al. [5] used ray tracing and finite difference methods to numerically simulate the interaction between acoustic waves and vortices. It was found that when the characteristic radius of the vortex was far larger than the wavelength of the acoustic wave, ray tracing was efficient in the extraction of the phase of the vortex acoustic signal. [PERSON] et al. [6] studied the influence of factors such as the characteristic radius of the vortex, vortex field type, and Mach number on the extraction of vortex acoustic signal characteristics based on ray acoustics theory. [PERSON] et al. [7, 8] simulated the ray trajectory and signal changes in acoustic signals passing through underwater steady-state vortex fields to establish a mapping relationship between the phase characteristics of vortex-acoustic signals and the characteristic parameters of vortex fields. However, a low Mach number of underwater vortices seriously weakens the phase characteristics of vortex acoustic signals. Additionally, due to the dynamic changes and severe fading of vortices in underwater acoustic channels, it is difficult to extract phase characteristics using traditional array signal processing methods. Various methods have become available for monitoring vortex currents, including the satellite remote sensing technique [9, 10, 11, 12], the Argo profiling floats technique [13, 14, 15], and ocean acoustic tomography [16, 17, 18]. However, each of these methods has its intrinsic limitations. For instance, the monitoring based on satellite remote sensing is not real-time; the Argo profiling floats technique requires manual round-trip measurements which can be labor-intensive; and ocean acoustic tomography is costly. Time-reversal mirror (TRM) technology, utilizing the time-reversal symmetry of acoustic waves, has been widely applied in underwater communication, acoustic imaging, and target localization [19, 20, 21]. Some scholars have also applied it to the extraction of underwater vortex acoustic signal characteristics. [PERSON] et al. [22] demonstrated, through ultrasonic experiments, that dual-time-reversal mirror technology can be used to amplify the phase changes in acoustic signals originated from vortex fields.