Abstract
Wave boundary conditions near the point of separation at a sharp edge are carefully examined, with new insights being derived for some common flow-tone situations. Application of the continuity of velocity principle enables the amplitude and phase of the instability wave to be related to the acoustic driving wave phasor. Likewise, continuity of shear stress leads to a mathematical dependence of shear layer dynamics on upstream wall boundary layer parameters. Some surprising results: (1) An instability wave driven near the point of separation is found to move initially at half the velocity expected from linear theory. (2) Although resonator-controlled flow tones operate at levels above the nonlinear saturation point for shear layer instability, they can exist only for shear layers that would otherwise be highly unstable. Some longstanding mysteries cleared up: (1) Why unflanged resonators (e.g., coke bottles) resist excitation by flow at grazing incidence. (2) Why flow-tone spectra are nearly pure sine waves, even for multimode cavity systems.
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