# Characteristics of Magnetic Fields Induced by the Wake of an Underwater Vehicle
## 5 Conclusions  
By using the co-simulation method of multiple physical fields, this study numerically simulated the wake magnetic field of the SUBOFF scale model (which is considered the research object), analyzed its time-frequency domain characteristics, and evaluated the wake magnetic field characteristics of underwater vehicles during constant-speed direct navigation and accelerated direct navigation.  
The results show that the frequency of the wake magnetic field of an underwater vehicle is not a single frequency point but is concentrated in the band spectrum of 0-5 Hz, which is a low-frequency signal. The frequency of the wake magnetic field is related to the speed of an underwater vehicle. The higher the speed, the smaller the barycenter frequency of the magnetic field is, but the larger the bandwidth is. When the underwater vehicle moved at speeds of 2, 2.5, and 3 m/s, the barycenter frequencies of the wake magnetic field were 2.20, 2.03, and 1.99 Hz, respectively, and the half-energy bandwidths were 0.86, 1.63, and 2.42 Hz, respectively.  
Different locations of the magnetic field monitoring points lead to different time-frequency domain distributions of the observed wake magnetic field. The magnetic fields generated by the underwater vehicle at the head and tail were strong, and the magnetic field directly above it was weak. When an underwater vehicle accelerates, the wake magnetic field increases, and the growth rate increases with increasing acceleration. When the underwater vehicle moved for a duration of 3.5 s at accelerations of 1, 2, and 3 m/s\({}^{2}\), the average magnetic field increased by 42.6, 94.0, and 139.7%, and the growth rates of the wake magnetic field were 1.78 \(\times\) 10\({}^{-11}\), 3.77 \(\times\) 10\({}^{-11}\), and 5.55 \(\times\) 10\({}^{-11}\) T/s, respectively.  
Figure 16: Magnetic field time-domain diagram of submarine movement with different accelerations at monitoring point A.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Acceleration (m/s\({}^{2}\))** & **1** & **2** & **3** \\ \hline Magnetic Field Size (T) & 9.88 \(\times\) 10\({}^{-12}\) & 1.34 \(\times\) 10\({}^{-11}\) & 1.66 \(\times\) 10\({}^{-11}\) \\ \hline Increase in Percentage (\%) & 42.6 & 94.0 & 139.7 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Wake magnetic field size and increase percentage under different accelerations in 3.5 s of movement.  
Therefore, a detection method based on the wake magnetic field is more appropriate for the process of acceleration and other manipulation motions of underwater vehicles.  
Specific contributions from the authors are as follows: conceptualization, M.P., J.H. and Q.Z.; methodology, Z.L. and B.H.; software, B.H.; validation, Y.X.; formal analysis, Q.D.; writing--original draft preparation, B.H.; writing--review and editing, B.H.; All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the National Natural Science Foundation of China (grant no. 6210012494).  
Not applicable.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.