The dynamics of quantised vorticity in neutron star interiors is at the heartof most pulsar glitch models. However, the large number of vortices (up to$\approx 10^{13}$) involved in a glitch and the huge disparity in scalesbetween the femtometer scale of vortex cores and the kilometre scale of thestar makes quantum dynamical simulations of the problem computationallyintractable. In this paper we take a first step towards developing a mean fieldprescription to include the dynamics of vortices in large scale hydrodynamicalsimulations of superfluid neutron stars. We consider a one dimensional setupand show that vortex accumulation and differential rotation in the neutronsuperfluid lead to propagating waves, or `avalanches', as solutions for theequations of motion for the superfluid velocities. We introduce an additionalvariable, the fraction of free vortices, and test different prescriptions forits advection with the superfluid flow. We find that the new terms lead tosolutions with a linear component in the rise of a glitch, and that, inspecific setups, they can give rise to glitch precursors and even to decreasesin frequency, or `anti-glitches'.
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