Superfluid vortex nucleation in He-3 flow

The flow of a superfluid past a solid boundary can generate vortices, with a key criterion being that the local flow speed reaches the speed of sound (Landau). However, the physical mechanism underlying this vortex generation remains unresolved. We consider the canonical problem of uniform flow past an impenetrable planar wall, to examine the vortex nucleation process generated by a solid obstruction moving through a superfluid. A linear stability analysis is conducted of this uniform two-dimensional flow governed by the Gross–Pitaevskii equation (GPE). This shows that the flow is marginally stable to two-dimensional, normal-mode perturbations. Direct numerical solutions of the GPE confirm this finding for small perturbations of finite amplitude. They also reveal the existence of a critical amplitude above which instabilities, in the form of vortices, are nucleated at the solid wall in finite time. Once nucleated, these vortices convect away from the solid wall with infinite initial speed. The physical mechanism underlying this nonlinear phenomenon is discussed, and a proposal is advanced to deepen its understanding.The flow of a superfluid past a solid boundary can generate vortices, with a key criterion being that the local flow speed reaches the speed of sound (Landau). However, the physical mechanism underlying this vortex generation remains unresolved. We consider the canonical problem of uniform flow past an impenetrable planar wall, to examine the vortex nucleation process generated by a solid obstruction moving through a superfluid. A linear stability analysis is conducted of this uniform two-dimensional flow governed by the Gross–Pitaevskii equation (GPE). This shows that the flow is marginally stable to two-dimensional, normal-mode perturbations. Direct numerical solutions of the GPE confirm this finding for small perturbations of finite amplitude. They also reveal the existence of a critical amplitude above which instabilities, in the form of vortices, are nucleated at the solid wall in finite time. Once nucleated, these vortices convect away from the solid wall with infinite initial speed. The physical mechanism underlying this nonlinear phenomenon is discussed, and a proposal is advanced to deepen its understanding.

Journal of Fluid MechanicsJul 17, 20260 citations

Metastable vortex in superfluid 3 He-B

Григорий Ефимович Воловик, M.M. Salomaa

ZhETF Pisma RedaktsiiuJan 1, 19870 citations

Scenario for a quantum phase slip in superfluid He4

S. Burkhart, M. Bernard, Olivier Avenel +1 more

Slips of the superfluid wave-function phase occur when the flow velocity through an aperture exceeds a critical threshold ${\mathit{v}}_{\mathit{c}}$ . We propose a phase slip mechanism in which a microscopic vortex half ring is nucleated at the wall of the aperture. Its subsequent trajectory is described. The properties of the vortex close to the wall are inferred from the Gross-Pitaevskii equation and yield, at T\ensuremath{\sim}0.1 K, a vortex radius at nucleation of 14 \AA{} and a critical velocity of 21 m/s, in agreement with experiment.Slips of the superfluid wave-function phase occur when the flow velocity through an aperture exceeds a critical threshold ${\mathit{v}}_{\mathit{c}}$. We propose a phase slip mechanism in which a microscopic vortex half ring is nucleated at the wall of the aperture. Its subsequent trajectory is described. The properties of the vortex close to the wall are inferred from the Gross-Pitaevskii equation and yield, at T\ensuremath{\sim}0.1 K, a vortex radius at nucleation of 14 \AA{} and a critical velocity of 21 m/s, in agreement with experiment.

Physical Review LettersJan 17, 199430 citations

Slips of the superfluid wave-function phase occur when the flow velocity through an aperture exceeds a critical threshold

{\mathit{v}}_{\mathit{c}}

. We propose a phase slip mechanism in which a microscopic vortex half ring is nucleated at the wall of the aperture. Its subsequent trajectory is described. The properties of the vortex close to the wall are inferred from the Gross-Pitaevskii equation and yield, at T\ensuremath{\sim}0.1 K, a vortex radius at nucleation of 14 \AA{} and a critical velocity of 21 m/s, in agreement with experiment.