Intrinsic compressibility effects on spectral characteristics of wall pressure fluctuations beneath turbulent boundary layers

Intrinsic compressibility (IC), associated with changes in fluid volume, has often been overlooked in high-speed turbulent boundary layers (TBLs). To quantify this critical effect on the spectrum of wall pressure fluctuations (WPFs), direct numerical simulations of zero-pressure-gradient flat-plate turbulent boundary layers were conducted, covering four freestream Mach numbers Ma = 0.5–8 and four wall temperature conditions Tw/Tr = 0.25–1. The results demonstrate that wall cooling under high-speed conditions markedly enhances IC effects. This enhancement is manifested through the emergence of alternating positive and negative dilatational structures and changes in the characteristic length scale. Furthermore, IC effects induce distinct local humps in the WPF frequency spectra, which lead to the failure of the well-known Goody model in accurately predicting the spectral features. Under wall cooling conditions, spectral energy in the wavenumber–frequency space becomes more concentrated, peak amplitudes are enhanced, and a distinct overlap between the acoustic and convective regions is observed. Moreover, IC effects cause the slow acoustic waves to become progressively submerged within the convective ridge, while the fast acoustic waves shift toward it, thereby intensifying the coupled interaction between acoustic waves and convective vortices.