Superfluid spherical Couette flow

Abstract

We solve numerically for the first time the two-fluid Hall-Vinen-BekarevichKhalatnikov (HVBK) equations for an He-II-like superfluid contained in a differentially rotating spherical shell, generalizing previous simulations of viscous spherical Couette flow (SCF) and superfluid Taylor-Couette flow. The simulations are conducted for Reynolds numbers in the range 1 × 10 2 6 Re 6 3 × 10 4 , rotational shear 0.1 6 Ω/Ω 6 0.3, and dimensionless gap widths 0.2 6 δ 6 0.5. The system tends towards a stationary but unsteady state, where the torque oscillates persistently, with amplitude and period determined by δ and Ω/Ω. In axisymmetric superfluid SCF, the number of meridional circulation cells multiplies as Re increases, and their shapes become more complex, especially in the superfluid component, with multiple secondary cells arising for Re > 10 3 . The torque exerted by the normal component is approximately three times greater in a superfluid with anisotropic Hall-Vinen (HV) mutual friction than in a classical viscous fluid or a superfluid with isotropic Gorter-Mellink (GM) mutual friction. HV mutual friction also tends to 'pinch' meridional circulation cells more than GM mutual friction. The boundary condition on the superfluid component, whether no slip or perfect slip, does not affect the large-scale structure of the flow appreciably, but it does alter the cores of the circulation cells, especially at lower Re. As Re increases, and after initial transients die away, the mutual friction force dominates the vortex tension, and the streamlines of the superfluid and normal fluid components increasingly resemble each other. In non-axisymmetric superfluid SCF, three-dimensional vortex structures are classified according to topological invariants. For misaligned spheres, the flow is focal throughout most of its volume, except for thread-like zones where it is strain-dominated near the equator (inviscid component) and poles (viscous component). A wedge-shaped isosurface of vorticity rotates around the equator at roughly the rotation period. For a freely precessing outer sphere, the flow is equally strain-and vorticity-dominated throughout its volume. Unstable focus/contracting points are slightly more common than stable node/saddle/saddle points in the viscous component, but not in the inviscid component. Isosurfaces of positive and negative vorticity form interlocking poloidal ribbons (viscous component) or toroidal tongues (inviscid component) which attach and detach at roughly the rotation period. 222

Continuous-wave gravitational radiation from pulsar glitch recovery

“…While it is unknown what triggers the collective unpinning, it is likely to excite a non-axisymmetric flow for two generic reasons. (1) Pinning causes the crust and superfluid to rotate differentially, inevitably driving non-axisymmetric meridional circulation and even turbulence, as observed in laboratory experiments (Munson & Menguturk 1975;Nakabayashi 1983;Junk & Egbers 2000) and numerical simulations (Peralta et al 2005(Peralta et al , 2006aMelatos & Peralta 2007;Peralta et al 2008;Peralta & Melatos 2009) of spherical Couette flow.…”

Pulsar timing noise and the minimum observation time to detect gravitational waves with pulsar timing arrays

“…The electromagnetic braking torque creates a crust-core shear layer that excites turbulence in the high-Reynolds number superfluid (Peralta et al 2005(Peralta et al , 2006aMelatos & Peralta 2007;Peralta et al 2008). The turbulent condensate reacts back to produce angular momentum fluctuations in the crust, which are observed as timing noise (Greenstein 1970;Melatos & Peralta 2010).…”

An Unstable Superfluid Stewartson Layer in a Differentially Rotating Neutron Star

“…We ignore vortex pinning and proton-neutron entrainment for simplicity, although recent work shows it to be important (Sedrakian & Sedrakian 1995;Andersson & Comer 2001). We adopt no-slip and no-penetration boundary conditions for the normal fluid component (velocity v n ) and nopenetration for the superfluid component (velocity v s ), ignoring the small tension force to reduce the order of the equation for v s by one (see Henderson et al (1995) and Peralta et al (2008) for a discussion). The mutual friction force is taken to have the anisotropic Hall-Vinen form (∝ω s × ω s × v ns , with v ns = v n − v s and ω = ∇ × v s ; Hall & Vinen 1956a, 1956b, with B = 10 −2 , and B = 10 −4 (Andersson et al 2007).…”