Refractive index fluctuation spectrum of lightwave propagation in supersonic compressible turbulent flow

When an aircraft flies at supersonic speed, a boundary layer is formed around the vehicle. The boundary layer gradually transitions to compressible turbulence near the aircraft wall. An aero-optical effect occurs when a beam passes through compressible turbulence, potentially causing wavefront distortion. Thus, the refractive index spectrum is very important in aero-optical research. In this paper, the general form of the refractive index function is derived from the velocity structure function of compressible flow. Although the general form of the refractive index spectrum is derived, it cannot be used in practice and can only predict a power law. This power law shows that the slope of the spectrum is related not only to −11/3 but also to −(m+2). In practice, the refractive index spectrum experienced by a propagating beam due to compressible turbulence near an aircraft wall is described by the autocorrelation function of the refractive index, which proves that m = 7/3 in this type of turbulence. In contrast to the traditional turbulent atmospheric spectrum, this study considers not only the temperature spectrum but also the pressure spectrum.