## 4 Numeric Analysis
### Effects of Sauwater Turbulence and Beam Parameters on Channel Capacity  
Figure 6 illustrates the impact of the dimensionless structural parameters \(\alpha\) on the channel capacity of the RCDPPGV carrier with different values of the channel numbers M. Figure 6 shows that the channel capacity in the \([-10,10]\) interval of \(\alpha\) is a nonlinear function of \(\alpha\) and reaches two maximum values at \(\mid\alpha\mid\) = 1. The difference value between the maximum channel capacity of each link increases with the number of OAM channels M. However, with the decrease in \(\mid\alpha\mid\) value, channel capacity tends to be constant, this constant is channel capacity at \(\mid\alpha\mid\) = 0. This result indicates that the link with single-position power Gaussian vortex has maximum channel capacity. Similar to any other type of beam [9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22], Figure 6 shows that the channel capacity also increases with the increase in channel number. Figure 7 shows that channel capacity decays rapidly as absorption increases. Seawater absorption has a great influence on the channel capacity, so in the detector design of the underwater communication system, it should take into account the inconsistency between the absorption of the offshore area and the open sea area. Figure 5: BER of the coaxial double-position power Gaussian vortex carrier communication link versus dissipation rate of the mean-squared temperature \(\chi_{T}\) for different topological charge of vortex. Figure 6: Channel capacity of the link with the coaxial double-position power Gaussian vortex carrier versus dimensionless parameter \(\mid\alpha\mid\)= 1 for different channel numbers M.  
Figure 8 shows the channel capacity of the RCDPPGV carrier versus the initial beam width \(w_{0}\) for different values of received diameter D. We can find that the channel capacity of the link with RCDGV carrier decreases with increase in the \(w_{0}\). This phenomenon can be explained as follows: when the initial beam size \(w_{0}\) is larger, the difference of turbulent seawater within the beam diameter is also larger. Of course, the wave front distortion of the transmitting beam is also large, so that the difference between signal probability and crosstalk probability tends to zero [30]. Figure 8 also shows that the channel capacity of the link with RCDPPGV carrier increases with an increase in D. This result can be explained by the following reasons: because the channel of OAM mode with higher topological charge is farther away from the axis of communication link [1; 26], the receiver with the larger receiving aperture can receive the information of the OAM mode channel with higher topological charge. In Figure 8, we investigate the effects of the temperature-salinity contribution ratios and different wavelength \(\lambda\) on the channel capacity of the RCDPPGV carrier in the \"seawater light transmission window\". Similar to any other type of beam [9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21], Figure 8 shows that the channel capacity of the RCDPPGV carrier increases with increasing \(\lambda\). This is because the long-wavelength beam has lower scintillations [25]. As \(\varpi\) increases, channel capacity decreases. This study is similar to studies for the single vortex information carrier [9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21], and salinity fluctuations have a greater impact on the channel capacity with a larger number of channels. In Figure 9, we investigate the effects of the outer scale of turbulence \(L_{0}\) and the inner scale of turbulence \(\eta\) on the channel capacity of RCDPPGV carrier. From Figure 5, we can see that the value of the channel capacity increases with an increase in \(\eta\) and a decrease in \(L_{0}\). This shows that the channel capacity increases with the increase in the inner scale of turbulence.