Turbulent flat-plate boundary layer flows have been widely employed for numerical validation in the aero-optical field. In present study, the laminar-to-turbulent evolution induced by wavy roughness in high-Reynolds-number supersonic freestream is investigated using a numerical technique based on the fifth-order weighted compact nonlinear scheme (WCNS-E-5). The computational procedure and post-processing method are described in detail, and the acquired instantaneous flow structure and statistical data are compared with other theoretical, experimental, and numerical results to demonstrate the feasibility of predicting turbulence using WCNS-E-5. Further, to reduce the computational resources required to simulate turbulent flow, a velocity correlation function is introduced to decrease the computational domain in the spanwise direction. Additionally, the effects of different grid sizes on the simulation results are examined by reducing the number of cells in the streamwise, wall-normal, and spanwise directions. Finally, the authors conduct a tentative investigation into the aero-optical effects of the laminar-to-turbulent flowfield using a ray-tracing method, considering both the feasibility of aero-optical detection and the effect of grid scale on the time-averaged imaging quality, as well as a deeper probe into the characteristic structures reflected by aero-optical frequency spectrum. The results elucidated that the wall-normal grid number has the strongest influence on the transitional location, and undoubtedly affects wavefront aberrations. However, different gird scales lead to similar aero-optical spectrum, and revealed the Kolmogorov-type turbulence at small-scale regime. As a prelude to further aero-optical simulations of wall-bounded flows, the current study provides some reference for the code validation process and aero-optical interrogation.
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