  We investigate the global transition from a turbulent state of superfluid
vorticity to a laminar state, and vice versa, in the outer core of a neutron
star. By solving numerically the hydrodynamic Hall-Vinen-Bekarevich-Khalatnikov
equations for a rotating superfluid in a differentially rotating spherical
shell, we find that the meridional counterflow driven by Ekman pumping exceeds
the Donnelly-Glaberson threshold throughout most of the outer core, exciting
unstable Kelvin waves which disrupt the rectilinear vortex array, creating a
vortex tangle. In the turbulent state, the torque exerted on the crust
oscillates, and the crust-core coupling is weaker than in the laminar state.
This leads to a new scenario for the rotational glitches observed in radio
pulsars: a vortex tangle is sustained in the differentially rotating outer core
by the meridional counterflow, a sudden spin-up event brings the crust and core
into corotation, the vortex tangle relaxes back to a rectilinear vortex array,
then the crust spins down electromagnetically until enough meridional
counterflow builds up to reform a vortex tangle. The turbulent-laminar
transition can occur uniformly or in patches; the associated time-scales are
estimated from vortex filament theory. We calculate numerically the global
structure of the flow with and without an inviscid superfluid component, for
Hall-Vinen and Gorter-Mellink forms of the mutual friction. We also calculate
the post-glitch evolution of the angular velocity of the crust and its time
derivative, and compare the results with radio pulse timing data, predicting a
correlation between glitch activity and Reynolds number.
