Structure of the refractive index distribution of the supersonic turbulent boundary layer

• The refractive index of supersonic turbulent boundary layer is measured.
• The power spectrum of the refractive index is analyzed.
• The structure function of the refractive index is analyzed.
• The characteristic length along vertical direction is analyzed.

The refractive index field of supersonic turbulent boundary layer with Mach number 3 is measured with the nanoparticle-based planar laser scattering technique, and its structure is investigated from the viewpoints of power spectrum, structure function and correlation function. The power spectrum along streamwise direction shows evident power behavior in a broad region of wavenumber, and the power exponent varies from −1.9 to −1.7 in the logarithmic region. The dominant structures is revealed using the pre-multiplied spectrum, and the length of the largest structure is about 1.2δ (δ is the thickness of the boundary layer). The structure function of the refractive index along streamwise direction is computed and an analytic expression is suggested to fit the experimental results, which is a modification of the Tatraski model. The power spectrum is computed with the fitting expression and its behavior is analyzed. The characteristic length along normal direction is studied with the linking equation in aero-optics. This length is defined with normal integral of correlation coefficient, and the results with two slightly different definitions of correlation coefficient are compared.