Aerodynamic Sound Radiated from a Turbulent Boundary Layer

Abstract

It is predicted, using two different types of simple argument, that the fluctuations in pressure upon a rigid plane boundary produce no contribution to the radiated sound field. The first is an acoustical argument involving the reflection of normal dipoles in the surface, and the second, concerned with the dynamics of the turbulent flow, suggests that the integrated correlation of the pressure fluctuations vanishes. Recent wind tunnel experiments by Harrison, however, offer little indication of support to the latter result (derived for a semi-infinite flow region), and some tentative suggestions are made concerning the resolution of this apparent paradox. An estimate is found for the acoustical energy radiated by the fluctuating shear stresses on a semi-infinite flat plate, along which a turbulent boundary layer is developing, and this is compared with the quadrupole radiation from the turbulence itself. It is found that the aerodynamic surface sound is relatively unimportant, indicating that, in the flow past an aerofoil, the principal source of sound radiation may lie in the fluctuations in net lift per unit length on the aerofoil as a whole.