  Many natural and engineering systems involve the mixing of two fluid streams,
in which the effects of density and viscosity gradients play important roles in
determining flow stability. We perform linear stability calculations for a jet
emerging into an ambient medium of a different viscosity but the same density.
These calculations are intended to isolate the effects of viscosity variation
alone. 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, the thickness over which the viscosity change occurs, and
radial shifts in velocity profiles, on the growth of axisymmetric and helical
modes. Additional terms in the disturbance kinetic energy equation that
represent the coupling between the velocity fluctuations and the viscosity
field are shown to be responsible for the additional destabilization. Radial
shifts in velocity profile that represent real effects likely to be encountered
in experiments are shown to be strongly destabilizing. In all cases, the
temporal growth rates of axisymmetric and helical mode are very close, except
at low Reynolds numbers. Spatio-temporal analysis in the complex wavenumber
plane suggests that for sufficiently large ambient viscosity, low-viscosity
jets become absolutely unstable. Over a wide range of parameters, two modes of
absolute instability exist simultaneously, with an axisymmetric mode predicted
to dominate a helical mode. Over a certain narrower space, the helical mode
dominates. The transition boundary for absolute/convective instability is
compared with recent experiments, and the results are found to in reasonable
agreement for the transition of the helical mode, when velocity profiles are
used that correspond to the similarity solution for development of the boundary
layer under a spatially variable viscosity.
