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

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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="bold-italic">β</mml:mi> </mml:mrow> </mml:math> between −0.81 and +0.68 at a wall-parallel plane located at a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi mathvariant="bold-italic">x</mml:mi> <mml:mn mathvariant="bold">2</mml:mn> <mml:mo>+</mml:mo> </mml:msubsup> <mml:mo>≈</mml:mo> <mml:mn mathvariant="bold">250</mml:mn> </mml:mrow> </mml:math> . 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.