We consider the linear stability of a cylindrical rotating jet of pure superfluid held together by surface tension. A necessary and sufficient condition for stability to axisymmetric disturbances is derived which corresponds to that of a classical inviscid fluid. For axisymmetric disturbances we find that the vortex tension does not affect the range of unstable axial wave numbers, only the temporal growth rate and the most critical wave number. A sufficient condition for the stability of a general disturbance is derived which corresponds to that of a classical inviscid fluid. We find for non-axisymmetric disturbances, that the vortex tension increases the range of unstable wave numbers. The temporal growth rates of the unstable azimuthal modes increase with vortex tension.
Henderson, K., & Barenghi, C. F. (2002). The stability of a superfluid rotating jet. Journal of Physics A: Mathematical and General, 35(45), 9645-9655. https://doi.org/10.1088/0305-4470/35/45/311