Temporal instability modes of supersonic round jets

Abstract

In this study, a comprehensive inviscid temporal stability analysis of a compressible round jet is performed for Mach numbers ranging from 1 to 10. We show that in addition to the Kelvin–Helmholtz instability modes, there exist for each azimuthal wavenumber three other types of modes (counterflow subsonic waves, subsonic waves and supersonic waves) whose characteristics are analysed in detail using a WKBJ theory in the limit of large axial wavenumber. The theory is constructed for any velocity and temperature profile. It provides the phase velocity and the spatial structure of the modes and describes qualitatively the effects of base-flow modifications on the mode characteristics. The theoretical predictions are compared with numerical results obtained for an hyperbolic tangent model and a good agreement is demonstrated. The results are also discussed in the context of jet noise. We show how the theory can be used to determine a priori the impact of jet modifications on the noise induced by instability.