Stability of high Reynolds number flow past a circular aperture

An analysis is made of the canonical problem of flow at very high Reynolds number past a circular aperture in a thin rigid wall. The motion is incompr essible, and the shear layer over the aperture is treated as a vortex sheet separating two parallel flows of unequal mean velocities, Viscosity is neg lected except for its role in shedding vorticity from the upstream semicirc ular edge of the aperture. Nominally steady flow is unstable, and often acc ompanied by large-amplitude self-sustaining oscillations at certain discret e frequencies, whose values are governed by a mechanism involving the perio dic shedding of vorticity from the leading edge of the aperture and feedbac k of pressure disturbances produced by interaction of the vorticity with th e downstream edge. Admissible frequencies are identified with the real part s of complex characteristic frequencies of the linearized equation of motio n of the vortex sheet. These eigenfrequencies are also poles of the Rayleig h conductivity of the aperture, and their dependence on the mean velocity r atio across the aperture is calculated for the first four 'operating stages ' of the motion. Results are presented in both graphical and tabular forms to facilitate their ready incorporation into numerical models of more compl icated flow problems. The investigation completes the linearized study of t his problem initiated by Scott, which dealt with forced, time-harmonic osci llations of the shear layer.