## 4 Results and Discussion  
The numerical results for the scintillation index of an UWOC system with spherical wave propagation in weak anisotropic turbulence are discussed in this section. The key parameters used in the simulation are listed in Table 1, and according to [45; 46; 47], the structure parameter \(C_{n}^{2}\) is \(7\times 10^{-17}\), unless special instructions are given. In addition, the unit of the aperture diameter is in millimeters [29; 48]. The influence of the outer scale on the scintillation index of a spherical wave under the conditions of different anisotropic factors is depicted in Figure 1. As we can see from this figure, the scintillation index of a spherical optical beam increases as the outer scale \(L_{o}\) increases. For instance, when \(\mu_{x}=1.01\) and \(\mu_{y}=1\), the scintillation index with an outer scale of 0.5 m is 0.0291 and when the outer scale becomes 3 m, the scintillation index increases to 0.0295. This phenomenon can be explained by the fact that the outer scale is the upper limit of the inertial zone and the refracting power of turbulence is directly limited by the outer scale. Therefore, a larger outer scale results in more severe scintillation. In addition, from Figure 1 we obtain that the scintillation index of the beam propagating in isotropic turbulence is more significant than that in anisotropic turbulence. Note that this conclusion has also been obtained in previous studies [44; 49]. For a fixed anisotropic factor in the \(x\)-direction, the larger anisotropic factor in the \(y\)-direction induces a smaller scintillation index. This phenomenon is also suitable for the anisotropic factor in the \(x\)-direction. Therefore, we conclude that anisotropic turbulence is helpful for spherical wave propagation in seawater. The reason for this phenomenon is that anisotropy changes the focusing properties of oceanic turbulence. Figures 2 and 3 show the relationship between the outer scale \(L_{o}\) and the scintillation index under different aperture diameters and wavelengths, respectively. Obviously, the scintillation index increases with increasing outer scale, as shown in Figure 1. Note that this trend is subdued due to the specific parameter values. Furthermore, the aperture averaging has a mitigating effect on the scintillation index, as shown in Figure 2. The larger aperture diameter decreases the scintillation index significantly. The scintillation index for the 532, 1064 and 1550 nm wavelengths are depicted in Figure 3, showing that the scintillation index decreases as the wavelength increases. This phenomenon is because shorter optical wavelengths are more susceptible to oceanic turbulence than longer optical wavelengths. The longer the optical wavelength, the smaller the fluctuation of the overall variance of \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Figure** & \(\lambda\) **(nm)** & \(L\) **(m)** & \(D\) **(cm)** & \(L_{i}\) **(mm)** & \(L_{o}\) & \(\mu_{x}\) & \(\mu_{y}\) \\ \hline Figure 1 & 532 & 10 & 1 & 10 & [0.5, 3] & 1, 1.01, 1.02 & 1, 1.03, 1.04 \\ Figure 2 & 532 & 10 & 1, 2, 3 & 10 & [0.5, 3] & 1 & 1.2 \\ Figure 3 & 532, 1064, 1550 & 10 & 1 & 10 & [0.5, 3] & 1 & 1.2 \\ Figure 4 & 532 & 10 & 1 & [2, 10] & 10 & 1, 1.6, 1.8 & 1, 12, 1.4 \\ Figure 5 & 532 & 10 & 1, 2, 3 & [2, 10] & 10 & 1 & 1.2 \\ Figure 6 & 532, 1064, 1550 & 10 & 1 & [2, 10] & 10 & 1 & 1.2 \\ Figure 7 & 532 & 10 & 1, 1.1, 1.2, 1.28, 1.29, 1.3, 2 & [2, 10] & 10 & 1 & 1,2 \\ Figure 8 & 532 & 10 & 1 & [2, 10] & 10 & 1, 1.4 & 1, 1.2 \\ Figure 9 & 532 & 10 & [1, 5] & 10 & 10 & 1, 1.4, 1.5, 1.6 & 1, 1.1, 1.2, 1.3 \\ Figure 10 & 532 & [10, 20] & 1 & 10, 15, 20 & 1, 5, 10 & 1 & 1.2 \\ Figure 11 & 532 & 10 & 1 & [2, 10] & [10, 30] & 1 & 1.2 \\ Figure 12 & 532 & [10, 30] & 1 & 10 & 10 & 1 & 1.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Key parameters used in calculations..  
Figure 1: Scintillation index of a spherical wave versus the outer scale for different anisotropic factors.