  Neutron star glitches are commonly believed to occur, when angular momentum
is transferred suddenly from the star's interior to the crust by the collective
unpinning and repinning of large numbers of superfluid vortices. In general,
the pinning potential associated with nuclei in the crustal lattice varies as a
function of radius. We explore vortex dynamics under these conditions by
solving the three-dimensional Gross-Pitaevskii equation in a rotating, harmonic
trap with an axisymmetric `moat' of deeper pinning sites on an otherwise
uniform, corotating pinning grid. The moat is designed to resemble crudely a
radially dependent pinning profile in a neutron star crust, although the values
of the pinning potential are not astrophysically realistic due to computational
constraints. It is shown that vortices accumulate in the moat, inducing large
differential rotation which can trigger mass unpinning events. It is also shown
that the system self-adjusts, such that the net vortex flux out of the system
is the same with and without a moat, as the trap spins down, but glitches are
less frequent and larger when the moat is present. The results, generated for
an idealized system, represent a first step towards including stratified
pinning in quantum mechanical models of neutron star glitches.
