Based on the generalized Huygens-Fresnel principle and the theoretical model of atmospheric turbulence,the analytical expression of the spiral spectrum and the expression of the light intensity of the Gaussian vortex beam in the non-Kolmogorov atmospheric turbulence with a slant path are derived,and the distribution rules of spiral spectrum and light intensity after the transmission of the vortex beam are numerically simulated.The effects of each beam parameter and atmospheric turbulence on the spiral spectrum dispersion are analyzed.The results show that with the increase of the transmission distance,the dispersion of the spiral spectrum is stronger.When the transmission distance increases to a certain distance,the spiral spectral components gradually tend to be uniform distribution, and the light intensity gradually presents a Gaussian distribution.Increasing the initial topological charge and wavelength of the beam can effectively reduce the dispersion degree of the spiral spectrum after transmission.When the zenith angle gradually increases to π/2,the transmission mode is horizontal transmission,and the dispersion degree of spiral spectrum is significantly increased.The larger the refractive index structure constant at the ground and the smaller the inner scale,the more serious the dispersion of the spiral spectrum after transmission,while the influence of the outer scale on the spiral spectrum is very small.