On the Rayleigh conductivity of a bias-flow aperture

An analysis is made of the attenuation of sound by vorticity production in a bias flow aperture. A modified form of the Cummings equation describing unsteady flow through a small aperture is used to extend the linear theory of the bias flow conductivity of a circular aperture in a thin wall of Howe (1979. On the theory of unsteady high Reynolds number flow through a circular aperture. Proceedings of the Royal Society of London A 366, 205-233) to a wall of arbitrary thickness and to examine the influence acoustic nonlinearity within the aperture. Numerical results are compared with existing analytic predictions of linear theory. It is shown that attenuations predicted by both linear and nonlinear theories agree over a wide range of incident acoustic pressures, approaching in amplitude that required to maintain the steady mean flow through the aperture. The dominant nonlinear effect is a small reduction (less than about 5%) in the mean bias flow velocity. Application of the Cummings equation in the linear regime leads to a new, simple formula for the bias flow conductivity for a screen of finite thickness.