Acoustic modes in jet and wake stability

Abstract : Motivated by recent studies that have revealed the existence of trapped acoustic waves in subsonic jets (Towne et al. J. Fluid Mech. vol 825, 2017, p. 1113-1152), we undertake a more general exploration of the physics associated with acoustic modes in jets and wakes, using a double vortex-sheet model. We show how jets and wakes may both behave as waveguides under certain conditions, emulating ducts with soft or hard walls, with the vortex-sheet impedance providing effective 'wall' conditions. We consider, in particular, the role that upstream-travelling acoustic modes play in the dispersion-relation saddle points that underpin the onset of absolute instability. The analysis illustrates how departure from duct-like behaviour is a necessary condition for absolute instability, and this provides a new perspective on the stabilising and destabilising effects of reverse flow, temperature ratio and compressibility; it also clarifies the differing symmetries of jet (symmetric) and wake (antisymmetric) instabilities. An energy balance, based on the vortex-sheet impedance, is used to determine stability conditions for the acoustic modes: these may become unstable in supersonic flow due to an energy influx through the shear layers. Finally, we construct the impulse response of flows with zero and finite shear-layer thickness. This allows us to show how the long-time wavepacket behaviour is indeed determined by interaction between Kelvin-Helmholtz and acoustic modes.
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Eduardo Martini, André Cavalieri, Peter Jordan. Acoustic modes in jet and wake stability. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2019, 867, pp.804-834. ⟨10.1017/jfm.2019.148⟩. ⟨hal-02351684⟩

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