## 3 Results and Discussion
### Spacing Ratio  
As mentioned earlier, the transverse arrangement of wind turbine arrays can improve the average efficiency of the wind turbines. The following study focuses on the spacing ratio between the wind turbine arrays in the transverse direction, with the aim of examining the enhancement effect. The spacing between wind turbines has an important impact on the entire transverse wind turbine array. The spacing ratio between VAWTs is expressed as L/D, where L is the distance between the centers of the wind turbines, and D is the maximum rotational diameter of the Nautilus wind turbine. In this study, wind turbine array models with L/D ratios of 1.2, 1.5, and 2 are investigated. The power coefficients of wind turbine arrays with different L/D ratios are shown in Figure 8. It can be seen from the figure that the efficiency curve of the array has some similarity with the efficiency curve of a single wind turbine. The efficiency reaches its highest value at TSR = 0.6, and the average efficiency of the entire array reaches 28.87% when L/D = 1.2. As the spacing between wind turbines decreases, the average power coefficient of the entire wind turbine array continues to increase, indicating that the more compact the spacing between two wind turbines, the higher the performance of the entire wind turbine array can be improved [31]. To clarify the enhancement effect, the concept of wind turbine power gain factor (_TPGF_) is introduced to evaluate the improvement of the dual wind turbine system's overall power output. The _TPGF_ is expressed as follows:  
\[TPGF=\frac{C_{P}(average)}{C_{P}}-1 \tag{5}\]  
The power coefficient comparison between wind turbine arrays and single wind turbines at the optimal TSR = 0.6 is shown in Figure 9. It is clear from Figure 9 that the wind turbine array has enhanced performance, with stronger enhancement at smaller spacing ratios. When L/D = 1.2, the power gain factor (_TPGF_) of the dual Nautilus wind turbine array reaches 10.2%. The closer and more compact the spacing between two wind turbines, the stronger the enhancement effect. However, in practical engineering applications, there should be a sufficient safety distance between two rotors to prevent any potential danger. To further elucidate the enhancement effect of wind turbine clusters, this paper explains it from the post-processing of the cross-sectional velocity wake field. Figure 10 shows the velocity contour of wind turbine sections with different spacing ratios, where the spacing between wind turbines is shown in Figure 10a, and 2D represents the spacing between the centers of the wind turbines perpendicular to the wind direction. The airflow passes through the wind turbine group with a certain spacing, and the wind turbines rotate clockwise. The flow field bends obliquely upward, showing the asymmetry of the wake field distribution, as indicated by the black arrows in Figure 10a,b. According to the Bernoulli principle, the smaller the spacing, the faster the wind speed, and the darker the color in the wake velocity field. The arrow represents the vector diagram of particle velocity. The downstream wind turbine 2 is not only affected by the incoming wind speed, but also by the flow direction generated by the rotation of the upstream wind turbine 1, which promotes, rather than hinders, the performance of the wind turbine as indicated by the black circle in Figure 10c. The smaller the spacing between wind turbines, the stronger this enhancement effect. Wind turbines 1 and 2 can obtain energy from neighboring wake  
Figure 8: Comparison of average power coefficients at different spacing ratios. Figure 9: Comparison of _TPGF_ of wind turbines with different spacing ratios. fields. This gain effect is not possible with standalone wind turbines and horizontal-axis wind turbine groups, which explains the essence of the enhanced effect of the transverse vertical-axis wind turbine group. To further investigate the flow characteristics of wind turbine groups, a velocity normalization analysis of the downstream wake was conducted.