Extracting dominant turbulent structures in supersonic flow using two-dimensional Fourier transform

A new image process for quantifying both convection velocities (U_C) and scales (λ_d) of turbulent structures captured in a fast-framing schlieren movie is presented. We obtained 90 time-series schlieren images of a transverse jet into a Mach 2 supersonic flow with 1-MHz sampling. The schlieren images captured not only the shock and expansion waves but also the turbulent structures within the jet and the boundary layer. The image intensities were extracted along the outer edges of the jet and the boundary layer and were remapped as a time–space intensity map. The time–space map exhibited swept stripe patterns, indicating that stable turbulent structures were periodically generated and convected downstream. The angle and interval of the stripe patterns were efficiently extracted using the two-dimensional Fourier transform, which corresponded to U_C and λ_d of the dominant structures. The zero-padding fast Fourier transform and the sub-pixel estimation of the spectral peak positions in the Fourier domain improved the accuracy for evaluating the angle and interval of the stripes, which resulted in the accurate evaluation of U_C and λ_d. The proposed method was validated by comparing U_C obtained using the proposed method to those obtained via schlieren image velocimetry for both the transverse jet and the supersonic boundary layer.