Analysis Of The Propagation Of Typical Beams In Compressible Turbulence

When the air velocity in turbulence approaches or exceeds the speed of sound,the turbulence exhibits compressibility,thus termed compressible turbulence.Compressible turbulence can impact the transmission of optical signals,essentially causing optical distortions induced by aerodynamics.The impact of compressible turbulence on an optical beam can be predicted through the refractive index spectrum power spectrum of turbulence.Compressible turbulent air,due to its high flow velocity,is considered compressible turbulence,while classical atmospheric turbulence is incompressible.This difference results in the power spectrum describing the refractive index of atmospheric turbulence being inapplicable to compressible turbulence.Therefore,deriving the refractive index spectrum for compressible turbulence is of significant importance for studying the boundary layer effect of light beams.In the paper,under the condition of supersonic turbulence flow(Ma > 1),based on the theory of flat plate boundary layer flow and the characteristic that the velocity divergence of compressible turbulence is non-zero,the general forms of structure functions and spectrum for compressible turbulence are derived.By incorporating the first-order fluctuation moment of the refractive index,a refractive index spectrum form is derived.Using this spectrum,the paper predicts the behavior of beams transmission in turbulence and explores the characteristics of beams transmission,as well as methods to improve the quality of beam transmission.The main research content and achieved research results include the following aspects:1.The physical properties of non-zero divergence for compressible turbulent gas velocity are considered,and the structure function of vector fields is derived.The structure function is analogized to refractive index field,providing the fundamental form of the refractive index structure functions for compressible turbulence.The basic power-law composition of the refractive index spectrum for compressible turbulence is also elucidated.Taking into account the factors affecting the spectrum power-law,such as the fluctuation of temperature and pressure,a specific form of the refractive index spectrum for compressible turbulence is proposed.Comparing the power-law spectrum with experimental data yielded good fit results.Additionally,based on the refractive index spectrum,wave structure functions and coherence radius for plane waves,spherical waves,and Gaussian waves in compressible turbulence are derived.This allows for assessing the strength and variability of compressible turbulence,which in turn influences the choice of optical transmission theory applications.2.Based on the generalized Huygens-Fresnel principle,an analytical expression for the intensity distribution of a Gaussian beam’s transmission in compressible turbulent environments is derived.the impact of turbulence and beam parameters such as turbulence intensity,wavelength,and transmission distance on optical power transmission are analyzed.The study also investigated beam spreading and drift in compressible turbulence.In regions of weak fluctuation turbulence,the Rytov theory is used to derive an analytical expression for the scintillation index of optical transmission in weak compressible turbulence.In regions with moderate to strong fluctuation turbulence,a modified Rytov theory is introduced,incorporating a spatial filtering function to filter out vortex scales that do not contribute to scintillation effects in moderate to strong turbulence.A scintillation index model for optical beam transmission in weak-moderate-strong compressible turbulence is established.A comparison is made with classical scintillation theory results,showing good fit.By using the probability density distribution of optical intensity in turbulence along with scintillation theory,the study predicted the average signal-to-noise ratio and error rate of optical signals in compressible turbulence.This provides a theoretical foundation for the establishment of laser communication systems.3.According to the anisotropic principle of optical turbulence,the isotropic compressible turbulence spectrum is extended to anisotropy.The equations of the wave structure function and coherence radius of the beam in the anisotropic turbulence are derived,and the mathematical expressions of the intensity,central transmittance and spot energy of the beam transmission are derived accordingly.The transmission characteristics of the beam are discussed,and the transmission and energy retention of the beam transmission are analyzed.Furthermore,the mathematical model of beam expansion and drift and the scintillation index model in weak-medium-strong turbulence fluctuations are re-established.The influence of anisotropic factors on various characteristics of beam transmission are analyzed,which can more realistically predict the transmission of beams in compressible turbulence.4.By utilizing the characteristic of temporal variation in turbulence,a half-Gaussian probability density distribution function for turbulence anisotropic factors is designed.A qualitative analysis is conducted to understand the actual variations in anisotropic factors fluctuations along the optical beam transmission path.The discussion centers on the impact of anisotropic factor fluctuations on the predictions made by optical beam transmission theories.Optical results are predicted using the probability density distribution of the anisotropic factors.A comparison is made between the optical characteristics predicted using the classical approach of anisotropic factor expectations and probability density distribution method,and the differences between the two methods are analyzed.This contributes to a better understanding of the boundary layer effects on optical beams.