On the Production of Sound by Turbulent Boundary Layer Flow over a Compliant Coating

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Abstract
A theory is proposed of the generation of sound by turbulent boundary layer flow over a nominally plane, compliant wall coating. It is argued that, at sufficiently low mean flow Mach numbers, the principal noise production mechanism involves the scattering of energy into sound from the hydrodynamic region of the wall pressure fluctuations by time dependent irregularities in the free surface of the coating induced by the turbulent flow. The effective noise sources are equivalent to a distribution of aerodynamic dipoles over the surface of the coating whose axes are parallel to the wall. The far field acoustic pressure spectrum, and the wavenumber-frequency wall pressure spectrum in the acoustic domain are expressed in terms of the behaviour of the wall pressure spectrum in the hydrodynamic domain. A simple empirical model of the hydrodynamic region, defined in terms of measurable parameters, is used to obtain explicit representations of the acoustic spectra.

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