The influence of the density ratio on the linear frequency response of low-density jets

Low-density jets support global self-sustained oscillations when the jet-to-ambient density ratio is sufficiently small, a phenomenon that has been linked to the presence of a region of local absolute instability in the underlying parallel base flow. However, the use of local stability analysis requires introducing ad-hoc criteria to match the experimental observations (see Coenen \& Sevilla, J.~Fluid Mech.\ 713, 2012, and references therein). In this work we therefore use a global approach, where the wavepacket structures are temporal eigenmodes of the linearized equations of motion in a 2D domain. The resulting eigenvalue spectra show that, when the density ratio is decreased, a discrete eigenmode becomes increasingly dominant, eventually reaching a positive growth rate for a certain critical density ratio. For the particular case of a He/air jet, this critical density ratio, as well as the corresponding oscillation frequency, is in good quantitative agreement with the experiments of Hallberg \& Strykowski (J.~Fluid Mech.\ 569, 2006). The influence of the density ratio on the linear frequency response of the jet under globally stable conditions is also investigated.