# Characteristics of Magnetic Fields Induced by the Wake of an Underwater Vehicle
## 4 Results and Discussions
### Characteristics of the Wake Magnetic Field
#### 4.2.3 Effect of Acceleration on the Wake Magnetic Field  
Figure 14 shows the underwater vehicle accelerating at 1, 2, and 3 m/s\({}^{2}\). When the acceleration changes, the time domain curves of the magnetic field at different observation points are shown below. We observed that when the underwater vehicle begins to accelerate, the wake magnetic field shows a short and sudden increase, which is attributed to the transfer of energy to the surrounding waters by the underwater vehicle from unforced to stressed. This results in a wide range of flow disturbances, leading to a sudden increase in the wake magnetic field. Before the underwater vehicle passes through the observ  
Figure 14: Magnetic field time domain diagrams at different monitoring points when the submarine moves with different accelerations. (**a**) a = 1 m/s\({}^{2}\); (**b**) a = 2 m/s\({}^{2}\); and (**c**) a = 3 m/s\({}^{2}\). Figure 13: The magnetic field time domain and power spectrum of the submarine passing through monitoring point A at different speeds. (**a**) Time domain and (**b**) power spectrum. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Speed (m/s)** & **2** & **2.5** & **3** \\ \hline Barycenter Frequency (Hz) & 2.20 & 2.03 & 1.99 \\ \hline Half-Energy Bandwidth (Hz) & 0.86 & 1.63 & 2.42 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Barycenter frequency and half-energy bandwidth of the wake magnetic field at different speeds. field is mainly determined by the disturbance of the first flow field. When it passes through the observation point, the magnetic field is mainly determined by the wake flow field. Therefore, in the above figure, the magnetic field of observation point B at the front end of the curve is the largest, and that of observation point D at the back end of the curve is the largest. Figure 15 shows the comparison of the magnetic fields of the underwater vehicle when it passed through magnetic field monitoring points B, C, and D at different accelerations. Notably, when the submarine passed directly below the monitoring point, the magnetic field decreased obviously; before and after the submarine passed through the monitoring point, the greater the acceleration, the larger the magnetic field and the greater the growth rate were. As the wake of the underwater vehicle at monitoring point A is fully developed, the influence of acceleration on the wake magnetic field was analyzed. Figure 16 shows the variation in the magnetic field with time under different accelerations at monitoring point A. Notably, the growth rate of the magnetic field increases obviously with increasing underwater vehicle acceleration: when the submarine moves at accelerations of 1, 2, and 3 m/s\({}^{2}\), the growth rates of the wake magnetic field are 1.78 \(\times\) 10\({}^{-12}\), 3.77 \(\times\) 10\({}^{-12}\) and 5.55 \(\times\) 10\({}^{-12}\) T/s, respectively, as presented in Table 4. We verified the above conclusions by measuring the magnetic field growth at different accelerations at monitoring points B, C and D.  
Notably, when the underwater vehicle moved at a uniform speed of 3 m/s, the average magnetic field at monitoring point A was 6.93 \(\times\) 10\({}^{-12}\) T. In the study of the accelerated motion of underwater vehicles, we assumed that the initial velocity was 3 m/s; subsequently, the vehicle moved at different accelerations. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Acceleration (m/s\({}^{2}\))** & **1** & **2** & **3** \\ \hline Growth Rate at Point A (T/s) & 1.78 \(\times\) 10\({}^{-12}\) & 3.77 \(\times\) 10\({}^{-12}\) & 5.55 \(\times\) 10\({}^{-12}\) \\ \hline Growth Rate at Point B (T/s) & 2.01 \(\times\) 10\({}^{-12}\) & 5.05 \(\times\) 10\({}^{-12}\) & 7.36 \(\times\) 10\({}^{-12}\) \\ \hline Growth Rate at Point C (T/s) & 2.34 \(\times\) 10\({}^{-12}\) & 6.23 \(\times\) 10\({}^{-12}\) & 7.60 \(\times\) 10\({}^{-12}\) \\ \hline Growth Rate at Point D (T/s) & 3.43 \(\times\) 10\({}^{-12}\) & 6.85 \(\times\) 10\({}^{-12}\) & 9.17 \(\times\) 10\({}^{-12}\) \\ \hline \hline \end{tabular}
\end{table}