Wall-Normal Velocity Correlations in a Zero Pressure Gradient Turbulent Boundary Layer

Abstract

An experimental campaign dedicated to the characterization of the wall-normal velocity correlations in a zero pressure gradient turbulent boundary layer was performed. A double set of laser Doppler velocimetry (LDV) benches were used to access two-point two-time correlations of the wall-normal velocity. The measurements analysis confirms several important hypotheses classically made to model wall pressure spectra from the velocity correlations. In particular, the ratio of the wall-normal Reynolds stress to the turbulent shear stress is confirmed to exhibit a large plateau in the logarithmic region. In addition, Taylor's hypothesis of frozen turbulence is well recovered for the wall-normal velocity fluctuations. The convection velocity for the wall-normal velocity fluctuations is also shown to evolve across the boundary layer, according to the mean velocity profile. Furthermore, the decorrelation time scale of velocity correlations appears to be increasing throughout the boundary layer thickness in accordance with the increase of the convection velocity. The results obtained with this original campaign will help improving models for wall pressure spectra, especially those based on the resolution of the Poisson equation for the pressure for which the wall pressure correlations are related to the wall-normal velocity correlations.