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We investigate the global transition from a turbulent state of superfluidvorticity to a laminar state, and vice versa, in the outer core of a neutronstar. By solving numerically the hydrodynamic Hall-Vinen-Bekarevich-Khalatnikovequations for a rotating superfluid in a differentially rotating sphericalshell, we find that the meridional counterflow driven by Ekman pumping exceedsthe Donnelly-Glaberson threshold throughout most of the outer core, excitingunstable Kelvin waves which disrupt the rectilinear vortex array, creating avortex tangle. In the turbulent state, the torque exerted on the crustoscillates, and the crust-core coupling is weaker than in the laminar state.This leads to a new scenario for the rotational glitches observed in radiopulsars: a vortex tangle is sustained in the differentially rotating outer coreby the meridional counterflow, a sudden spin-up event brings the crust and coreinto corotation, the vortex tangle relaxes back to a rectilinear vortex array,then the crust spins down electromagnetically until enough meridionalcounterflow builds up to reform a vortex tangle. The turbulent-laminartransition can occur uniformly or in patches; the associated time-scales areestimated from vortex filament theory. We calculate numerically the globalstructure of the flow with and without an inviscid superfluid component, forHall-Vinen and Gorter-Mellink forms of the mutual friction. We also calculatethe post-glitch evolution of the angular velocity of the crust and its timederivative, and compare the results with radio pulse timing data, predicting acorrelation between glitch activity and Reynolds number.Comment: (1) School of Physics, University of Melbourne, Parkville, VIC 3010,  Australia. (2) Departamento de Fisica, Escuela de Ciencias,Universidad de  Oriente, Cumana, Venezuela, (3) Department of Mechanical and Manufacturing  Engineering, University of Melbourne, Parkville, VIC 3010, Australia.  Accepted for publication in The Astrophysical Journal. 30 pages, 9 figures  (in jpg format

Transitions between Turbulent and Laminar Superfluid Vorticity States in the Outer Core of a Neutron Star