From shear stress to wall pressure spectra: a semi-analytical approach to account for mean pressure gradients in turbulent boundary layers

Abstract

This study offers a semi-analytical means to compute the wall pressure spectra beneath a turbulent boundary layer depending only on the latter’s Kármán number and dimensionless pressure gradient. By inclusion of the total mean shear profiles in a mixing length model, the velocity profiles can be reconstructed under adverse, zero- and favourable pressure gradients. These profiles serve as input to existing models of the wall pressure spectra and thus remove the need for experimental or numerical data. The modelled frequency spectra fairly estimate the level of the measured ones. The three typical regions of those spectra are recovered, although the overlap one is shorter than with experimental data, and the trends of pressure gradients effects are also observed. The wavenumber representation shows the effect of pressure gradients on the convective ridge structure as its aspect ratio increases from adverse to favourable ones. The same variation is observed in experimental data, and although the absolute values of the aspect ratios do not match, qualitative observations can be made.