Vortices, shocks and non-linear acoustic waves: the ingredients for resonance in impinging compressible jets

Compressible jets impinging on a perpendicular surface can produce high-intensity, discrete-frequency tones. The character of these tones is a function of nozzle shape, jet Mach number, impingement-plate geometry, and the distance between nozzle and plate. Though it has long been recognised that these tones are associated with a resonance cycle, the exact mechanism by which they are generated has remained a topic of some debate. In this work, we present evidence for a number of distinct tone-generation mechanisms, reconciling some of the different findings of prior authors. We demonstrate that the upstream-propagating waves that close resonance can be confined within the jet, or external to it. These waves can be either weak and relatively linear, or strong and nonlinear from their inception. The waves can undergo coalescence or merging, and in some configurations, pairs of waves rather than singletons appear. We discuss both historical and new evidence for multiple distinct processes by which upstream-propagating waves are produced: direct vortex sound, shock leakage, wall-jet-boundary fluctuations, and wall-jet shocklets. We link these various mechanisms to the disparate collection of upstream-propagating waves observed in the data. We also demonstrate that multiple mechanisms can be provoked by a single vortex, providing an explanation as to why sometimes pairs of waves or merging waves are observed. Through this body of work, we demonstrate that rather than being in opposition, the various pieces of past research on this topic were simply identifying different mechanisms that can support resonance.