TABLE OF CONTENTS Xavier Gloerfelt, Christophe Bogey, and Christophe Bailly
Impinging shear layers give rise to intense, self-sustained oscillations as well as noise radiation. Flow past a cavity belongs to this class of flows and has been extensively studied for the last 50 years because of its practical interest, its geometrical simplicity, and the diversity of the theoretical questions that it raises. The generic features are assessed in detail in the reviews of Rockwell and Naudascher (1978); Tam and Block (1978); Rockwell (1983); Komerath, Ahuja, and Chambers (1987); Howe (1997); or Colonius (2001).
The self-sustained oscillations arise from a feedback loop consisting of the following chain of events. The growth and convection of instability waves in the shear layer induce large-amplitude pressure disturbances as the vortical perturbations impinge on the downstream corner of the cavity. The upstream influence of the generated pressure fluctuations provides further excitation of the instabilities in the shear layer ? especially in its most receptive region near the upstream edge. A stable phase criterion is then installed between the downstream and the upstream edges of the cavity. This complex phenomenon is often greatly simplified to build lumped models such as the Rossiter formula (Rossiter 1964) in which the free-shear layer is viewed as two-dimensional and the recirculating flow is neglected. At high Mach numbers, this simple formula succeeds in predicting the admissible Strouhal numbers, although it provides no information on the amplitude of the self-sustained oscillations and fails to...
