Absolute instability of a viscous hollow jet

An investigation of the spatiotemporal stability of hollow jets in unbounded coflowing liquids, using a general dispersion relation previously derived, shows them to be absolutely unstable for all physical values of the Reynolds and Weber numbers. The roots of the symmetry breakdown with respect to the liquid jet case, and the validity of asymptotic models are here studied in detail. Asymptotic analyses for low and high Reynolds numbers are provided, showing that old and well-established limiting dispersion relations [J. W. S. Rayleigh, The Theory of Sound (Dover, New York, 1945); S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Dover, New York, 1961)] should be used with caution. In the creeping flow limit, the analysis shows that, if the hollow jet is filled with any finite density and viscosity fluid, a steady jet could be made arbitrarily small (compatible with the continuum hypothesis) if the coflowing liquid moves faster than a critical velocity.