Thermal nucleation of vortices in a uniform flow

Thermal and quantum nucleation of vortices in superfluids attracted the attention of theorists long ago (Iordanskii, 1965b; Langer and Fisher, 1967; Muirihead et al., 1984). The quantum nucleation of vortices by superflow in small orifices (Davis et al., 1992; Ihas et al., 1992) and by moving ions (Hendry et al., 1988) has been reported.

The process of vortex nucleation is crucial for onset of essential dissipation when superfluid velocities reach the critical velocity for penetration of vortices into a container. The original state is a metastable state with a persistent vortex-free superfluid flow. Vortex nucleation is necessary for transition to a state with a smaller superfluid velocity (and eventually to the stable equilibrium state with zero velocity) in the case of uniform flows in channels, or for transition to solid body rotation with an array of straight vortices parallel to the rotation axis in the case of rotating containers. In the process of vortex nucleation a small vortex loop appears, which grows in size. Eventually the vortex loop transforms to a straight vortex line in the case of rotation, or the vortex line crosses the channel crosssection decreasing the phase difference between ends of the channel by 2π (the phase slip). The latter process is illustrated in Fig. 11.1. Although vortex nucleation is a key process, which determines critical velocities, the problem of critical velocities does not reduce to the nucleation problem. The theory of critical velocities requires introduction of additional definitions and assumptions. One can find discussion of critical velocities with relevant references elsewhere (Donnelly, 1991; Varoquaux, 2015).

Vortex nucleation is possible due to either thermal or quantum fluctuations in the fluid. This section addresses the Iordanskii–Langer–Fisher theory of thermal nucleation (Iordanskii, 1965b; Langer and Fisher, 1967). The rate of thermal nucleation of vortices is governed by the Arrhenius law ∝ e −Em/T. The energetic barrier Em is determined by a maximum of the energy of a vortex loop in the process of its growth.