Sound Generated by Boundary-Layer Flow over Small Steps: Effect of Step Noncompactness
The effect of acoustically non-compact step height on sound generation in a turbulent boundary layer is studied by computing sound with a boundary-element method and comparing its results with those obtained with a compact-step-height assumption. When the ratio of acoustic wavelength to the step height is large, good agreements between the two methods in predicted sound spectra and directivities are found, thus validating the previous compact Green’s function solutions. Discrepancies between the two results become significant with decreasing �/h. For mildly non-compact step heights, the sound directivity for forward steps exhibits asymmetry, with the upstream side maintaining an approximate dipole shape while the rest significantly distorted. Dips in sound spectra and multiple lobes in directivity are observed along with significantly enhanced sound power when �/h is sufficiently small, indicating that edge-scattering becomes the dominant source mechanism. These results indicate that the compact-step-height assumption is generally applicable for underwater applications, where small Mach numbers give large �/h for most frequencies of interest. For air vehicles with large Mach numbers, its applicability is much more limited.