Rayleigh Conductivity and Self-Sustained Oscillations

The theory of self-sustaining oscillations of low Mach number, high Reynolds number shear layers, and jets impinging on edges and corners is discussed. Such oscillations generate narrow band sound, and are usually attributed to the formation of discrete vortices whose interactions with the edge or corner produce impulsive pressures that trigger the cyclic formation of new vorticity. A linearized analysis of these interactions is described in which free shear layers are treated as vortex sheets. Details are given for shear flow over wall apertures and shallow cavities, and for jet–edge interactions. The operating stages of the oscillations correspond to complex eigenvalues of the linear theory: for wall apertures and edge tones they are poles in the upper half of the complex frequency plane of the Rayleigh conductivity of the “window” spanned by the shear flow; for shallow wall cavities they are poles of a frequency-dependent drag coefficient. It is argued that the frequencies defined by the real parts of the complex frequencies at these poles determine the operating stage Strouhal numbers observed experimentally. Strouhal number predictions for a shallow wall cavity are in good agreement with data extrapolated to zero Mach number from measurements in air; edge tone predictions are in excellent accord with data from various sources in the literature.