On the structure of the turbulent boundary-layer wall pressure spectrum in the vicinity of the acoustic wavenumber

Abstract

Theoretical investigations of the wavenumber-frequency spectrum of wall pressure fluctuations induced by turbulent boundary-layer flows of low Mach number indicate the existence of a spectral peak at wavenumbers in the vicinity of the acoustic wavenumber. The peak is associated with large amplitude grazing, or ‘creeping’, acoustic waves and, according to Lighthill’s theory of aerodynamic sound, is of infinite, non-integrable intensity for a homogeneous boundary layer formed on an infinite, plane rigid wall. A review is given in this paper of theoretical attempts to determine the magnitude of the peak in real flows either by, (i) imposing a finite limit on the size of the boundary layer, or by (ii) taking account of the attenuation of the grazing acoustic waves by the turbulence through which they must propagate. An additional mechanism is also examined for boundary layers formed on large curved surfaces. This frequently occurs in applications, and surface acoustic creeping modes are then attenuated by losses due to radiation into the fluid. The influence of turbulence absorption is shown to be negligible, whereas the effects of finite boundary-layer size and wall curvature are found to be of comparable magnitudes, and are presumably the principal factors governing the height of the spectral peak for boundary layers formed on a rigid wall.