Hierarchical structure of the optical path length of the supersonic turbulent boundary layer

The optical path length (OPL) of supersonic turbulent boundary layer of Mach number 3.0 is obtained with the nanoparticle-based planar laser scattering technique, and its structure is analyzed within the framework of hierarchical symmetry assumption. Our result offers reasonable evidence for that the OPL obeys this assumption with parameter β depending on q. The scaling exponent ζ(q) of structure function is computed and compared with the theoretical prediction of She-Leveque model. The curve ζ(q) we obtained is convex and smaller than the theoretical value for small q, which is attributed to the large scale structure of the OPL.