Abstract:
The linear theory is developed of self-sustained oscillations of shear layers and jets incident on edges and corners at infinitesimal Mach number. These oscillations are sources of narrow-band sound. Detailed predictions are made of the operating stages for shear flows over wall apertures, shallow wall cavities, and for the classical edge tone, by modeling free shear layers by vortex sheets. Operating stages are identified with the poles of a certain impulse response function; the real parts of these poles determine the operating Strouhal numbers observed experimentally for the real, nonlinear system. The response function coincides with the Rayleigh conductivity of the window spanned by the shear flow for wall apertures and edge tones, and to a drag coefficient for wall cavities. Strouhal numbers predicted for a shallow wall cavity agree well with experimental data in air extrapolated to zero Mach number; edge-tone predictions are in excellent accord with data from various sources. In the latter case, the linear theory also agrees for all operating stages with an empirical, nonlinear model that takes account of the formation of discrete vortices in the jet. [Work supported by the Office of Naval Research.]