Universal form of the power spectrum of the aero-optical aberration caused by the supersonic turbulent boundary layer

Based on the measurement of one-dimensional (1D) optical path difference (OPD) of the supersonic turbulent boundary layer, an analytical form for the power spectrum of the two-dimensional (2D) OPD is obtained with its structure function and under the locally homogeneous isotropic assumption. The universality of this spectrum is argued, and its validity is checked by the comparison with experimental result. The potential applications of this model in theoretical and numerical studies are emphasized. Another contribution of this work is around the application of correlation function to analyzing the statistics of OPD. Based on our results and other results published elsewhere, we show that the OPD is often not stationary, and one should be cautious about using this tool. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)