Linear stability analysis of a low-viscosity jet emerging into a high-viscosity ambient fluid

Recent experiments with low-viscosity jets emerging into a high viscosity ambient medium have documented a transition from axisymmetric instabilities to helical instabilities, as the viscosity ratio M between the ambient and jet is increased. A single dominant frequency is observed in the near-field of the jet, suggesting that this may be a global mode. Global modes have been linked in other flows such as low-density jets and countercurrent shear layers to the presence of local absolutely unstable profiles. Accordingly, in this study, linear stability calculations of a low-viscosity jet emerging into a high-viscosity ambient are performed. We conduct a systematic study of the effect of ambient-to-jet viscosity ratio, jet Reynolds number, and the velocity profile specified by the shear layer thickness and inflection point location, on the growth of axisymmetric and helical modes. Spatio-temporal analysis in the complex wavenumber plane suggests that beyond a critical viscosity ratio, the flow becomes absolutely unstable, with the helical mode being dominant. The shear layer thickness, as well as the location of the inflection point, which is determined by the viscosity ratio in experiments, are shown to be critical factors in determining this critical value of viscosity ratio.