Reynolds Number Effects on the Spectra of Compressible Turbulent Boundary Layers

We study Reynolds number effects on pre-multiplied energy spectra of density corrected streamwise velocity in compressible turbulent boundary layers (CTBL). We demonstrate that different large-scale trends, as those for incompressible TBL, are associated with friction Reynolds numbers based on wall or freestream conditions, Reτ and Re* respectively. Notice that in CTBL Re* can be orders of magnitude larger than Reτ. The inner layer turbulence exhibits dependence on both Reynolds numbers. However, the strength of large turbulent structures, which is given by the magnitude in the spectral peak, depends only on the wall friction Reynolds number. The large scales in the log layer, for which the strength increases with Reτ , are modified through changes in local fluid properties such that the scale interaction near the wall is Re* dependent. That is, closer to the wall, the CTBL flow behaves like a Re*, an effectively larger Reynolds number flow, while closer to the freestream, the flow behaves like an Reτ flow. The present study highlights the inadequacy of using a univariate wavelength based on viscous, semi-local or outer length scales to differentiate small and large scales.