Wavenumber-frequency cross-spectra of correlated wall pressure and velocity components in varying external pressure gradients

Abstract

Synchronous wall-pressure and velocity measurements were acquired within a fully developed turbulent boundary layers over a smooth rigid surface under the effects of three mean pressure gradients. This allowed the development of a wavenumber-frequency cross-spectrum between the correlated pressure and velocity fluctuations. Measurement acquired for a friction Reynolds number of 3200–3300, and at a boundary layer parameter $\mathit{\beta }$ between −0.81 and +0.68 at a wall-parallel plane located at a ${\mathit{x}}_{\mathbf{2}}^{+}\approx \mathbf{250}$ . Results show that both the streamwise and wall-normal velocity components are of equal relative importance when correlated with wall-pressure fluctuations. The wavenumber-frequency spectra of the pressure-velocity cross-terms collapse on one another for the three pressure gradient cases; however, the sub-convective levels of pressure and streamwise velocity spectrum show elevated levels for the adverse pressure gradient case, as high as 10 dB, when compared to the favorable pressure gradient case.