  We study the motion of neutron superfluid vortices in a spinning-down neutron
star, assuming axisymmetry of the flow and ignoring motion of vortices about
the rotation axis. We find that the vortex array, if initially rectilinear, is
soon substantially deformed as the star spins down; vortices are swept outward
by the Magnus force, accumulating in regions of the inner crust where they pin,
accompanied by significant bending of the vortex array. As the star spins down
to below a spin rate of ~20 Hz (twice the spin rate of the Vela pulsar), the
Magnus and pinning forces gradually compress the vortex array into dense sheets
that follow spherical shells. In some cases, the vortex array bends on itself
and reconnects, forming one or more tori of vortex rings that contain
superfluid ``rivers" with significant angular momentum. Vortex sheets are
likely to form near the base of the inner crust, in the regime of nuclear
pasta.
