THE INFLUENCE OF TANGENTIAL MEAN FLOW ON THE RAYLEIGH CONDUCTIVITY OFAN APERTURE

An investigation is made of the influence of grazing mean flow on the Rayleigh conductivity of an aperture in a thin rigid plane. The fluid is assumed to be incompressible and inviscid, but the Kutta condition is applied to permit the generation of vorticity at the edge of the ap erture by an applied time-varying pressure field. Numerical results ar e given for a circular aperture in the two cases of (i) one-sided mean flow, when the aperture is spanned by a plane vortex sheet in the und isturbed state, and (ii) two-sided mean flow, when the mean velocity i s the same on both sides of the plane, so that the undisturbed motion is irrotational. In both cases there exist frequency ranges within whi ch perturbation energy is either absorbed or generated by the mean flo w. The numerical. results are supplemented by an approximate analytica l treatment of the same problem for a rectangular aperture of large as pect ratio (with its long edge transverse to the mean flow direction). The aperture flux for one-sided flow is shown to be absolutely unstab le, and may in principle be triggered by an arbitrary, small disturban ce in the mean stream. For two-sided flow the motion is conditionally unstable, in the sense that perturbations are amplified by the extract ion of energy from the mean flow only when the frequency of the applie d pressure lies in certain discrete bands.