# Characteristics of Magnetic Fields Induced by the Wake of an Underwater Vehicle
## 1 Introduction  
The movement of conductive seawater in a geomagnetic field produces a displacement current that produces a magnetic field corresponding to the seawater velocity field. This phenomenon was predicted by [PERSON] [1] and quantitatively measured by several researchers [2]. Based on this, scholars have conducted extensive research on the magnetic field related to moving seawater, including internal waves [3, 4], wind waves [5, 6], and ocean currents [7, 8]. In particular, a moving underwater vehicle can induce abundant disturbances in the surrounding fluids, resulting in long-term large-scale wakes, and such hydrodynamic disturbances produce an induction magnetic field under a geomagnetic field. This phenomenon was disregarded in the application of underwater target detection because of the limitation of the weak magnetic field detection capability. However, the development of an atomic magnetometer with measurement accuracy at the picotesla level provides more possibilities for applying this phenomenon to target detection areas [9]. In the future, the investigation of electromagnetic fields produced by moving seawater is expected to become an essential part of marine electromagnetic applications. The fluid field phenomenon is necessary to investigate the magnetic field induced by the wake flow of the vehicle. The free-surface Kelvin wake, generated by a ship or submarine, can spread over several kilometers and is sustained for more than ten minutes. This can be considered a steady signature for tracking the targets. Detecting such magnetic anomalous fields produced by wakes has been proposed as a potential method for detecting ships and submarines. [PERSON] [10] developed a mathematical model to calculate the electromagnetic signals induced by the wake of a ship in conductive seawater under a geomagnetic field. According to their research, the spectrum of an electromagnetic field canbe detected. [PERSON] and [PERSON] [11] proposed another mathematical model to describe the induction magnetic field in water at a finite depth and explored its behavior with respect to the environmental parameters and geometric characteristics of the moving object. The infinite-depth ocean model was also employed by [PERSON] and [PERSON] [12] and [PERSON] et al. [13]. [PERSON] and [PERSON] [14] investigated two parts of the induced electromagnetic fields: the attenuating oscillation of the free-surface Kelvin wake and the bipolar pulse of the localized volume wake. Near the sea surface, the magnitude of the former is typically a few hundred picotesla, while that of the latter could be ten-fold higher. Consistent with studies on the wake phenomenon of vehicles, the detection method for such a magnetic field has also improved. [PERSON] and [PERSON] [15] investigated the spectral characteristics of a magnetic field induced by the wake of a moving ship. Typically, the peak of the ship-induced magnetic field spectrum can be clearly distinguished from noise. [PERSON] and [PERSON] [16] proposed a multisensor arrangement of magnetic transducers to estimate the traveling direction of the vessel by detecting its magnetic wakes. The proposed method performed well in dealing with Gaussian white noise and various target cutting angles. As the hydrodynamic wake generated by submarine navigation can lead to a magnetic wake, it has all the characteristics of a hydrodynamic wake [17] and can be used for the detection of underwater targets and estimation of their physical parameters, such as the velocity, acceleration, and direction of movement [18]. In 2022, the pronounced range and intensity of the electromagnetic signatures in the near-field wake were obtained by multi-physics field coupling numerical simulations [19]. These scientific findings provided a conducive insight for lucidating the evolutions of the induced electromagnetic wake and assisted in further promoting the development of submersible non-acoustic detection.