  The dynamics of quantised vorticity in neutron star interiors is at the heart
of most pulsar glitch models. However, the large number of vortices (up to
$\approx 10^{13}$) involved in a glitch and the huge disparity in scales
between the femtometer scale of vortex cores and the kilometre scale of the
star makes quantum dynamical simulations of the problem computationally
intractable. In this paper we take a first step towards developing a mean field
prescription to include the dynamics of vortices in large scale hydrodynamical
simulations of superfluid neutron stars. We consider a one dimensional setup
and show that vortex accumulation and differential rotation in the neutron
superfluid lead to propagating waves, or `avalanches', as solutions for the
equations of motion for the superfluid velocities. We introduce an additional
variable, the fraction of free vortices, and test different prescriptions for
its advection with the superfluid flow. We find that the new terms lead to
solutions with a linear component in the rise of a glitch, and that, in
specific setups, they can give rise to glitch precursors and even to decreases
in frequency, or `anti-glitches'.
