  Superfluid hydrodynamics affects the spin-evolution of mature neutron stars,
and may be key to explaining timing irregularities such as pulsar glitches.
However, most models for this phenomenon exclude the global instability
required to trigger the event. In this paper we discuss a mechanism that may
fill this gap. We establish that small scale inertial r-modes become unstable
in a superfluid neutron star that exhibits a rotational lag, expected to build
up due to vortex pinning as the star spins down. Somewhat counterintuitively,
this instability arises due to the (under normal circumstances dissipative)
vortex-mediated mutual friction. We explore the nature of the superfluid
instability for a simple incompressible model, allowing for entrainment
coupling between the two fluid components. Our results recover a previously
discussed dynamical instability in systems where the two components are
strongly coupled. In addition, we demonstrate for the first time that the
system is secularly unstable (with a growth time that scales with the mutual
friction) throughout much of parameter space. Interestingly, large scale
r-modes are also affected by this new aspect of the instability. We analyse the
damping effect of shear viscosity, which should be particularly efficient at
small scales, arguing that it will not be sufficient to completely suppress the
instability in astrophysical systems.
