The low-frequency pressure fluctuations of near-equilibrium turbulent boundary layers

Abstract

The low-frequency pressure fluctuations generated by a range of roughness configurations are explored for flows of roughness Reynolds numbers over 200 and blockage ratios above 73. Two-point analysis of the pressure fluctuations reveals that surfaces with high frontal solidity, $\lambda$, and/or complex shear layer interactions near the elements, have structures which persist longer than structures on the smooth wall. A low-frequency pressure spectrum scaling based on the broadband convection velocity defect, $U_{\text{e}}-{\overline{U}}_{\text{c}_{\text{b}}}$, is proven effective for all rough surfaces and the smooth wall. Here $U_{\text{e}}$ is the boundary layer edge velocity, and ${\overline{U}}_{\text{c}_{\text{b}}}$ is the mean broadband convection velocity. A second scaling, which is more appropriate for a priori predictions, is also proposed. It uses the mean velocity defect, $U_{\text{e}}-{\overline{U}}$ (where ${\overline{U}}$ is the mean boundary layer velocity), first proposed for velocity profiles by Zagarola and Smits (J Fluid Mech 373:33–79, 1998). Both scalings are effective because they are based on velocity defects proportional to the outer-layer shear stress which generates the pressure fluctuations. A re-examination of the outer-layer wall-similarity in the context of these new findings suggests that this concept is limited to a narrow range of turbulent boundary layer flows.

Graphical abstract