Onset of global instability in low-density jets

In low-density axisymmetric jets, the onset of global instability is known to depend on three control parameters, namely the jet-to-ambient density ratio S, the initial momentum thickness theta(0) and the Reynolds number Re. For sufficiently low values of S and theta(0), these jets bifurcate from a steady state (a fixed point) to a self-excited Em oscillatory state (a limit cycle) when Re increases above a critical value corresponding to the Hopf point, Re-H. In the literature, this Hopf bifurcation is often regarded as supercritical. In this experimental study, however, we find that under some conditions, there exists a hysteretic bistable region at Re-SN < Re < Re-H, where Re-SN denotes a saddle-node point. This shows that, contrary to expectations, the Hopf bifurcation can also be subcritical, which we explore by evaluating the coefficients of a truncated Landau model. The existence of subcritical bifurcations implies the potential for triggering and the need for weakly nonlinear analyses to be performed to at least fifth order if one is to be able to predict saturation and bistability. We conclude by proposing a universal scaling for ReH in terms of S and theta(0). This scaling, which is insensitive to the super/subcritical nature of the bifurcations, can be used to predict the onset of self-excited oscillations, providing further evidence to support Hallberg & Strykowski's concept (J. Fluid Mech., vol. 569, 2006, pp. 493-507) of universal global modes in low-density jets.