The far-field sound from rough-wall boundary layers

The noise radiated by a turbulent boundary layer over a rough wall is shown to be characterized by a dipole surface source that, if the surface pressure is spatially homogeneous, can be specified by a convolution integral combining the surface pressure wavenumber spectrum and the wavenumber spectrum of the surface roughness slope. For random roughness elements with almost vertical sides, the surface slope has a wavenumber white spectrum and the radiated sound is directly proportional to the surface pressure spectrum multiplied by an acoustic efficiency factor (k(o)h)(2), where k(o) is the acoustic wavenumber and h is the geometrical r.m.s. roughness height. The theoretical result agrees with the roughness noise measurements of Smith et al. (Smith et al. 2008 AIAA paper no. 2008-2904) for all flow speeds and roughness element heights (in wall units) of k(g)(+) < 34. The theory can also be applied to wavy walls and this provides a new method for measuring the wavenumber spectrum of surface pressure fluctuations.