Wavelet analysis of high-speed transition and turbulence over a flat surface

Abstract

This paper presents a study of high speed boundary layers using the wavelet method. We analyze direct numerical simulation data for high-speed, compressible transitional, and turbulent boundary layer flows using orthogonal anisotropic wavelets. The wavelet-based method of extraction of coherent structures is applied to the flow vorticity field, decomposed into coherent and incoherent contributions using thresholding of the wavelet coefficients. We show that the coherent parts of the flow, enstrophy spectra, are close to the statistics of the total flow, and the energy of the incoherent, noise-like background flow is equidistributed. Furthermore, we investigate the distribution of the incoherent vorticity in the transition and turbulent regions and examine the correlation with the near-wall pressure fluctuations. The results of our analysis suggest that the incoherent vorticity part is not a random “noise” and correlates with the actual noise emanating from inside the boundary layer. This could have implications regarding our understanding of the physics of compressible boundary layers and the development of engineering models.