Abstract
An analysis is made of the effect of cross-sectional shape on the motion induced in a wall aperture by a pressure perturbation in the presence of high Reynolds number tangential flow. Previous studies for circular and rectangular apertures indicate that there is a transfer of energy from the applied perturbation to the mean flow (via the production of vorticity in the aperture) provided the Strouhal number based on aperture diameter and mean velocity is small. In this paper apertures are considered whose cross-sections are symmetrically tapered in a direction parallel to the mean flow. For highly tapered apertures of trapezoidal cross-section, it is found that low Strouhal number damping is confined to a smaller range of frequencies. Self-sustaining oscillations of the shear layers spanning the aperture can occur at certain discrete frequencies, which correspond to the real parts of complex eigenfrequencies of the aperture motion havingpositiveimaginary parts. The eigenfrequencies are poles of the Rayleigh conductivity, and are found to vary in proportion toU/L, whereUis mean flow speed andLis the maximum streamwise length of the aperture, but to be only weakly dependent on aperture shape.
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