## 4 Results and Discussion
the wavefront, and the more stable it is in spatial frequency, while the shorter the optical wavelength, the greater the fluctuation of the wavefront, and the more sensitive it is to the influence of turbulence. Therefore, we conclude that increasing the aperture diameter and the optical wavelength is an alternative method to mitigate the influence of oceanic turbulence on the UWOC system. In addtion, it can be concluded from Figures 1-3 that the outer scale has a small effect on the scintillation even neglected, which is similar to the previous studies [(35; 50)]. Figure 3: Scintillation index of a spherical wave versus the outer scale for different wavelengths. Figure 2: Scintillation index of a spherical wave versus the outer scale for different aperture diameters. To further investigate the influence of the inner scale on the scintillation, we plot the curve of the inner scale \(L_{i}\) versus the scintillation index under different anisotropic factors, as shown in Figure 4. Different from the influence of the outer scale, the inner scale shows the opposite trend, i.e., the scintillation index decreases as the inner scale increases. In addition, this declining trend levels off as the inner scale continue to increase. This can be explained by the fact that when the inner scale is non-zero, it serves as the lower limit of the inertial zone and governs the diffraction ability of turbulence. As the inner scale becomes larger, the diffraction distortion caused by the small vortices is weakened. In addition, both in the \(x\)-direction and in the \(y\)-direction, a spherical wave has a lower scintillation index when propagates in higher anisotropic oceanic turbulence. Moreover, the scintillation index of the beam propagating in anisotropic turbulence is always lower than its propagation in isotropic turbulence (\(\mu_{x}=\mu_{y}=1\)). This phenomenon is because anisotropy changes the focusing properties of oceanic turbulence. Anisotropic turbulence vortices act as lenses with a longer radius of curvature than isotropic turbulence vortices. The higher the anisotropy, the longer the radius of curvature, resulting in reduced amplitude fluctuations and thus lower scintillation index. The impact of the aperture diameter and optical wavelength on the scintillation index as a function of the inner scale is also demonstrated in Figures 5 and 6, respectively. Obviously, the scintillation index decreases along with the increase of the aperture diameter and wavelength, which further confirms our simulations in Figures 2 and 3. Note that the decreasing trend of scintillation index under different wavelengths is valid for a smaller value of the inner scale. However, this trend slows down when the inner scale is more prominent, since a coherence length change is mitigated. Increasing the aperture parameter significantly reduce the scintillation index shown in Figure 5. Moreover, the beam of smaller wavelength has better performance, as is shown in Figure 6. The above two figures are all conducted under anisotropic turbulence. To further consider the aperture averaging effect under isotropic turbulence (\(\mu_{x}=\mu_{y}=1\)), we studied the scintillation index after changing the aperture diameters under isotropic conditions, as shown in Figure 7. It is observed that the scintillation index under anisotropic oceanic turbulence is much smaller than that under isotropic turbulence, which is consistent with Figures 1 and 4. With the increase of the aperture diameters, the scintillation index of the beam propagating in isotropic decreases gradually and approaches that in anisotropic  
Figure 4: Scintillation index of a spherical wave versus the inner scale for different anisotropic factors. turbulence. In Figure 7, when aperture diameter \(D=1\) cm, the scintillation index at \(\mu_{x}=1\), \(\mu_{y}=2\) is lower than the scintillation index in isotropic. When the aperture diameter is 1.29 cm, the two curves almost coincide. Therefore, we can reduce the scintillation index by changing the aperture size in isotropic oceanic turbulence.