Improved equivalent optical turbulence method for anisotropic compressible and atmospheric turbulence under different beam transmission distances

The impact of different turbulence on beams can be seen as optical distortions caused by refractive index fluctuations around vortices in turbulence. Therefore, from the perspective of transmission effects, the transmission outcomes of beam in different turbulences can be mutually equivalent. Since the mechanisms of beam propagation in compressible turbulence are not yet fully understood and the relevant theories are not well-established, a preliminary analysis of beam transmission in compressible turbulence is necessary. This analysis will help understand the medium characteristics of compressible turbulence, particularly its similarities and differences with atmospheric turbulence, before the optical effects of compressible turbulence are fully resolved. This paper establishes a connection between anisotropic atmospheric turbulence and compressible turbulence parameters by utilizing the mature solutions of beam in anisotropic atmospheric turbulence. We then employ the optical parameters of anisotropic atmospheric turbulence to represent those in compressible turbulence, leveraging existing solutions to assess beam transmission in compressible turbulence. Building upon the original equivalent method, we extend the dimension of transmission distance, ensuring that beams equivalence is maintained across different turbulence regimes. The results indicate that the equivalent method can effectively adapt to compressible turbulence. By using the equivalent structure function, it is possible to represent compressible turbulence parameters with the atmospheric refractive index structure constant. This method also works across different transmission distances. The method facilitates finding various solutions for beam in compressible turbulence.