The influence of surface roughness on wall‐pressure fluctuations and the radiated sound from a turbulent boundary layer

Abstract

The noise and vibration produced during turbulent boundary‐layer flow over a nominally plane flexible surface are governed by the low wavenumber and acoustic regions of the wall‐pressure wavenumber‐frequency spectrum. In the case of a rough surface, the spectrum differs from that on a smooth wall on two counts: (i) the strengths of the turbulent Reynold stress fluctuations, which are ultimately responsible for the pressure field, are increased by the action of surface roughness; (ii) the pressure field produced by those enhanced pressure sources is redistributed in the wavenumber plane by diffraction by the roughness elements. The wall‐pressure spectrum can be expressed in the form P(k,ω) = P0(k,ω) + PR(k,ω), where P0 denotes the spectrum that would be associated with the roughness‐enhanced Reynolds stresses if the wall were assumed to be perfectly flat, and PR is the additional component due to the diffraction mechanism (ii). It will be shown that PR is expected to dominate the behavior of the wall press...