The influence of mean shear on unsteady aperture flow, with application to acoustical diffraction and self-sustained cavity oscillations

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Abstract
This paper discusses the linearized theory of unsteady flow through a two-dimensional aperture in a thin plate in the presence of a grazing mean flow on one side of the plate. The mean shear layer is modelled by a vortex sheet, and it is predicted that at low mean-flow Mach numbers there is a transfer of energy from the mean flow to the disturbed motion of the vortex sheet provided (i) the Kutta condition is imposed at the leading edge of the aperture, resulting in the unsteady shedding of vorticity from the edge, and (ii) the width of the aperture 2s satisfies ½ < 2s/λ < 1.1, where λ is the hydrodynamic wavelength of the disturbance on the vortex sheet within the aperture. The theory is used to examine the effect of mean shear on the diffraction of sound by a perforated screen, and to predict the spontaneous excitation and suppression of self-sustained oscillations in a wall-cavity beneath a nominally steady mean flow. In the latter case support for the proposed theory is provided by a favourable comparison of theoretical results with experimental data available in the literature.
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