# A Survey of Structure of Atmospheric Turbulence in Atmosphere and Related Turbulent Effects
## 4 Theoretical Studies of Combined Influence of Kolmogorov and Non-Kolmogorov Turbulence  
To conclude, the existence of non-Kolmogorov turbulence is an indisputable fact both theoretically and experimentally. As the measurement of atmospheric turbulence deepens and the understanding of atmospheric turbulence structure is further refined, various models describing atmospheric turbulence structure of Earth's atmosphere have been developed. [PERSON] and [PERSON] established a two-layer turbulence model based on the early measured results of atmospheric turbulence; that is, the turbulence in Earth's atmosphere is composed of Kolmogorov turbulence in the troposphere and \(-5\) non-Kolmogorov turbulence in the stratosphere. They further studied the combined effects of these two kinds of turbulence on infrared imaging [26]. Later, [PERSON] studied the combined effects of Kolmogorov turbulence in the troposphere and \(-5\) non-Kolmogorov turbulence in the stratosphere on star image jitters [87]. [PERSON] et al. modified the two-layer model from [PERSON] and [PERSON] based on the consistency between the refractive index fluctuation power spectrum and the structure function and the measurement results of [PERSON] et al. The influence of Kolmogorov turbulence in troposphere and \(-5\) non-Kolmogorov turbulence in the stratosphere on the fluctuation of starlight angle-of-arrival was studied [27]. [PERSON] et al. developed a three-layer atmospheric turbulence model of Earth's atmosphere based on recent measurements of atmospheric turbulence; that is, the turbulence in Earth's atmosphere is composed of the Kolmogorov turbulence in the boundary layer, the \(-10/3\) non-Kolmogorov turbulence in the free atmosphere, and the \(-5\) non-Kolmogorov turbulence in the stratosphere. Then, the logarithmic amplitude variance of the electromagnetic wave propagating in Earth's atmosphere was studied by using this model [88]. [PERSON] et al. studied the combined influence of Kolmogorov turbulence and non-Kolmogorov turbulence on space optical communication under the condition of weak fluctuations based on the three-layer model of atmospheric turbulence in satellite-Earth links [89]. Based on the study of [PERSON] et al., [PERSON] et al. also used a three-layer model to study the bit error rate of satellite-ground laser communication uplink under weak fluctuation conditions [90]. Our research group has also performed some studies on the basis of establishing a theoretical model of long-term beam spreading and scintillation index of Gaussian beam in the stratosphere non-Kolmogorov turbulence under the condition of weak fluctuations. The combined influence of Kolmogorov turbulence in troposphere and \(-5\) non-Kolmogorov turbulence in the stratosphere on satellite-Earth laser communication was studied based on a two-layer model of atmospheric turbulence with respect to the satellite-Earth link. The combined effects of tropospheric Kolmogorov atmospheric turbulence and stratosphere \(-5\) non-Kolmogorov atmospheric turbulence on long-term beam spreading [91] and the scintillation index of Gaussian beams were analyzed. On this basis, the effects of combined atmospheric turbulence on the performance of space-ground laser links were studied, and the bit error rate under the OOK system was analyzed [27; 92; 93]. Based on the three-layer combined atmospheric turbulence model, the intensity fluctuation and beam propagation of uplinks and downlinks under strong fluctuation regimes were analyzed, and the relationship between bit error rate and SNR of fading channels in satellite-based laser communication links was then analyzed. The influence of strong combined atmospheric turbulence on the angle-of-arrival fluctuation of uplinks and downlinks was also studied. Furthermore, the variance and time-frequency spectrum models of angle-of-arrival fluctuation for uplinks and downlinks under a strong fluctuation regime were established and analyzed theoretically [94; 95; 96].