Effects of the Convection and Decay of Turbulence on the Wall Pressure Wavenumber-Frequency Spectrum

Cross-spectral and cross-correlation data from experiments and numerical simulations have shown the turbulent wall pressure convection velocity to vary with the streamwise spatial separation ξ, due to the different spatial decays of turbulent structures in the inner and outer regions of the boundary layer. This effect is shown to have a significant impact on the distribution of energy in the wavenumber-frequency spectrum Φ(k1,ω). The overprediction of spectral levels at low wavenumbers using the standard Corcos model is shown to result from assuming a constant convection velocity in the cross spectrum. The spectral levels at subconvective and lower wavenumbers are shown to be directly influenced by the decay and convection of turbulence in both the inner and outer regions of the boundary layer. These results compare favorably with recent numerical results. The attenuations in the autospectrum due to finite sensors are shown not to be significantly influenced by this effect. Convection velocity measurements from past investigations that cover the range 285 ≤ Rθ ≤ 29,000 are compared, and an outer variable scaling is found to be the most effective for collapsing the data.