## 1 Introduction
In theory, further development of the propagation theory of passive conservative quantity has shown that although the Kolmogorov spectrum is important, it is only part of more general behavior of passive conservative quantity propagation in turbulence. At the same time, other theoretical studies further confirm this conclusion [14; 15; 16]. For example, when the atmosphere is in a relatively stable state that are not locally isotropic, the behavior is inconsistent with the Kolmogorov turbulence statistical law [14]. [PERSON] [16] conducted a numerical study on the power spectrum of internal gravity waves and the results confirmed the existence of a turbulent power spectrum with a power ratio of \(-5\), which corresponds to internal gravity waves (IGW). IGW are anisotropic structures. [PERSON] et al. [17; 18; 19] suggested a hypothesis that atmospheric coherent structures were principal causes of considerable deviations of the Kolmogorov and Obukhov constants from their standard values. Turbulence observed in a coherent structure is called coherent turbulence, which is different from noncoherent Kolmogorov turbulence. Its one-dimensional spectrum has one more rapid decrease in the inertia interval and lower contributions of small-scale components. Phase fluctuations of optical radiation in coherent turbulence are weaker as compared to the Kolmogorov one (due to lack in small-scale inhomogeneities). The combined influence of Kolmogorov and non-Kolmogorov turbulence on optical wave has been investigated along a slant or vertical path on the basis of further development of a propagation theory for optical wave in non-Kolmogorov turbulence, including beam spreading, intensity fluctuations, etc. [20; 21]. These studies were carried out by establishing a two-layer turbulence model based on the early observations of atmospheric turbulence. Namely the turbulence in the earth's atmosphere is composed of Kolmogorov turbulence (spectral exponent \(-11/3\)) in the troposphere and non-Kolmogorov turbulence (spectral exponent \(-5\)) in the stratosphere. The latest measurements showed that the atmosphere turbulence in the the boundary layer obeyed the Kolmogorov theory and that the atmosphere turbulence in the free troposphere was different from one in the stratosphere, both of which exhibited non-Kolmogorov properties. The more accurate three-layeratmospheric turbulence model was developed. The related works also were extended from the two-layer atmospheric turbulence model to the three-layer one, including scintillation index of a plane and spherical wave at large zenith angles, propagation of electromagnetic waves, etc. [22; 23; 24]. The fluctuation conditions also gradually expanded from weak to strong fluctuations. It is well-known that beam wander can cause time-varying power fades at the receiver terminal and further deteriorates the performance of satellite laser communication system. Meanwhile, beam wander also affects the acquiring probability, acquiring time, pointing accuracy, and tracking stability of the laser communication link and then degrades the performance of satellite laser communication pointing, acquiring, and tracking subsystem. Therefore, it is significant to study the combined influence of the three-layer atmospheric turbulence on the wander of the laser beam wave as the carrier wave in laser satellite communication. In this paper, a three-layer altitude-dependent power spectrum of refractive-index fluctuations for satellite-to-ground and ground-to-satellite links is modified, which is composed of the Kolmogorov power spectrum with an exponent value of \(-11/3\), non-Kolmogorov ones with exponent values of \(-10/3\) and \(-5\), corresponding to the boundary layer, the free troposphere, and the stratosphere in the aerospace, respectively. Using the Markov approximation, beam wander displacement variances of a Gaussian-beam wave propagating through non-Kolmogorov turbulence in the free troposphere and the stratosphere are derived, respectively.