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The interiors of mature neutron stars are expected to be superfluid.Superfluidity of matter on the microscopic scale can have a number of largescale, potentially observable consequences, as the superfluid component of thestar can now flow relative to the `normal' component that is tracked byelectromagnetic emission. The most spectacular of such phenomena are pulsarglitches, sudden spin-ups observed in many pulsars. A background flow of anormal-fluid component with respect to the superfluid is also known to lead toa number of instabilities in laboratory superfluids, possibly leading toturbulence and modifying the nature of the mutual friction coupling between thetwo fluids. In this paper we consider modes of oscillation in the crust andcore of a superfluid neutron star, by conducting a plane-wave analysis. Weexplicitly account for a background flow between the two components (as wouldbe expected in the presence of pinning) and the entrainment, and we considerboth standard (Hall-Vinen) and isotropic (Gorter-Mellink) forms of the mutualfriction. We find that for standard mutual friction there are families ofunstable inertial and sound waves both in the case of a counter-flow along thesuperfluid vortex axis and for counterflow perpendicular to the vortex axis andfind that entrainment leads to a quantitative difference between instabilitiesin the crust and core of the star. For isotropic mutual friction we find nounstable modes, and speculate that instabilities in a straight vortex array maybe linked to glitching behaviour, which then ceases until the turbulence hasdecayed.

Hydrodynamical instabilities in superfluid neutron stars with background flows between the components