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

We investigate the global transition from a turbulent state of superfluid vorticity (quasi-isotropic vortex tangle) to a laminar state (rectilinear vortex array), 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 that 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 (triggered by an unknown process) brings the crust and core into corotation, the vortex tangle relaxes back to a rectilinear vortex array (in ≲10⁵ s), and then the crust spins down electromagnetically until enough meridional counterflow builds up (after ≲1 yr) to reform a vortex tangle. The turbulent-laminar transition can occur uniformly or in patches; the associated timescales 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 (laminar) and Gorter-Mellink (turbulent) forms of the mutual friction. We also calculate the postglitch 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. Terrestrial laboratory experiments are proposed to test some of these ideas.