# A Survey of Structure of Atmospheric Turbulence in Atmosphere and Related Turbulent Effects
## 3 Theoretical Studies of Turbulent Effect
### Theoretical Studies of Non-Kolmogorov Turbulent Effect
established a theoretical model for calculating the spiral spectrum, also called the orbital angular momentum (OAM) spectrum, of a Laguerre-Gaussian (LG) beam after propagation through anisotropic non-Kolmogorov turbulence along a horizontal link [70]. In the study of optical wave propagation in non-Kolmogorov atmospheric turbulence, our research group has also performed some studies. The scintillation index of Gaussian beam, the temporal power spectrum of plane wave and spherical wave intensity fluctuations, the variance and temporal power spectrum of the angle-of-arrival fluctuation for plane wave and spherical waves, beam wander, and the two-frequency mutual correlation function of Gaussian beam were studied, respectively, by using Rytov perturbation approximation and a spectral analysis method [71; 72; 73; 74; 75; 76; 77]. With the further development of research, the characteristics of optical wave propagation in non-Kolmogorov atmospheric turbulence under strong fluctuation conditions have become the focus of research, and some research achievements have been obtained. [PERSON] et al. studied the coherence radius, phase structure function, and scintillation index of plane wave and spherical wave in non-Kolmogorov atmospheric turbulence under strong fluctuations by using universal von-Karman power spectrum [78]. Based on the universal von-Karman power spectrum, [PERSON] et al. studied the angle-of-arrival fluctuation variances of plane and spherical waves in non-Kolmogorov turbulence under strong fluctuation conditions by using the modified Rytov theory [79]. [PERSON] et al. also studied the influence of non-Kolmogorov atmospheric turbulence on angle-of-arrival fluctuations for plane wave and spherical wave under moderate to strong fluctuations, and a new analytical expression of variance was obtained [80]. [PERSON] et al. investigated the effects of moderate-to-strong non-Kolmogorov turbulence on the angle-of-arrival fluctuations for plane and spherical waves in detail both analytically and numerically. New analytical expressions for the variance of angle-of-arrival fluctuations were derived for moderate-to-strong non-Kolmogorov turbulence [81]. [PERSON] et al. studied the scintillation index of Gaussian beams in non-Kolmogorov atmospheric turbulence under strong fluctuation regimes by using a modified Rytov theory based on a non-Kolmogorov atmospheric turbulence power spectrum density [82]. [PERSON] et al. studied the temporal characteristics of angle-of-arrival fluctuations of plane and spherical waves in non-Kolmogorov atmospheric turbulence under strong fluctuation regime and obtained the temporal power spectrum expressions of angle-of-arrival fluctuation [83]. [PERSON] et al. studied the influence of non-Kolmogorov atmospheric turbulence on the plane wave and spherical wave structure functions under strong fluctuation regimes and then studied the influence of the modulation transfer function [84]. [PERSON] et al. theoretically derived a new power spectrum model of atmospheric turbulence and then used this spectral model to re-derive the expressions of plane wave and spherical wave scintillation index in non-Kolmogorov atmospheric turbulence under strong fluctuation regime [85]. [PERSON] et al. derived and further analyzed the scintillation index of Gaussian beams in a new non-Kolmogorov atmospheric turbulence with strong fluctuations by using a universal effective atmospheric turbulence power spectrum [86]. As previously mentioned, the theoretical research performed on propagation of optical waves in a Kolmogorov turbulent atmosphere is relatively early and mature. The theoretical research methods developed have been widely used in the study of optical wave propagation in non-Kolmogorov atmospheric turbulence. The statistical properties of optical wave are explored when the power law of refractive index fluctuation power spectrum deviates from -11/3. The atmospheric turbulent effects of plane wave, spherical wave, and Gaussian-beam wave have been studied more than that of special beams.