RAYLEIGH CONDUCTIVITY AND SELF-SUSTAINED OSCILLATIONS

The theory of self-sustaining oscillations of low Mach number, high Re ynolds number shear layers, and jets impinging on edges and corners is discussed. Such oscillations generate narrow band sound, and are usua lly attributed to the formation of discrete vortices whose interaction s with the edge or corner produce impulsive pressures that trigger the cyclic formation of new vorticity. A linearized analysis of these int eractions is described in which free shear layers are treated as vorte x sheets. Details are given for shear flow over wall apertures and sha llow cavities, and for jet-edge interactions. The operating stages of the oscillations correspond to complex eigenvalues of the linear theor y: for wall apertures and edge tones they are poles in the upper half of the complex frequency plane of the Rayleigh conductivity of the ''w indow'' 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 t hese poles determine the operating stage Strouhal numbers observed exp erimentally. Strouhal number predictions for a shallow wall cavity are in good agreement with data extrapolated to zero Mach number from mea surements in air; edge tone predictions are in excellent accord with d ata from various sources in the literature.