The equation of motion of a superfluid vortex in the local induction approximation includes terms describing the self-induced velocity, normal fluid friction, and the Magnus force. We integrate the equations of motion of an ensemble of vortices numerically in a spherical, Taylor-Couette geometry, starting from a regular, pinned array parallel to the rotation axis. The results are used to model the long-time-scale dynamics of a 1S0 superfluid in young (Crab-like) and adolescent (Vela-like) pulsars.