This paper investigates requirements for neutral acoustic stability in cavities with a transpiring wall where there is a mean flow in the absence of acoustic disturbances. The growth rates of the acoustic fields are also considered. The method of calculation utilizes time averages of the mass, momentum, and energy-conservation equations to second order in the acoustic-field quantities. It is found that growth rate and neutral stability may be expressed in terms of only first-order quantities. The results are shown to be in agreement with those calculated from first-order admittance considerations, but differ, in general, from those of Dyer, who uses a method of calculation similar to the present paper. The resolution of this conflict is discussed. The effect of mean flow is often of considerable importance, and the extent to which flow tends to excite or damp the acoustic field is related to mode configuration and flow-field geometry. Application to the problem of determining the acoustic response of burning rocket propellants is discussed.
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Cantrell et al. (1964) studied this question.