On pressure fluctuations in the near-wall region of turbulent flows

We study the near-wall behaviour of pressure spectra and associated variances in canonical wall-bounded flows, with a special focus on pipe flow. Analysis of the pressure spectra reveals the universality of small and large scales, supporting the establishment of $ k^{-1}$ spectral layers as predicted by fundamental physical theories. However, this universality does not extend to the velocity spectra (Pirozzoli, J. Fluid Mech. , vol. 989, 2024, A5), which show a lack of universality at the large-scale end and systematic deviations from the $ k^{-1}$ behaviour. We attribute this fundamental difference to the limited influence of direct viscous effects on pressure, with implied large differences in the near-wall behaviour. Consequently, the inner-scaled pressure variances continue to increase logarithmically with the friction Reynolds number as we also infer from a refined version of the attached-eddy model, while the growth of the velocity variance tends to saturate. Extrapolated distributions of the pressure variance at extremely high Reynolds numbers are inferred.