Vortex Tangle Dynamics Without Mutual Friction in Superfluid ⁴He

Abstract

Recently Davis et al. observed the free decay of the vortices at mK temperatures where the normal fluid density became vanishingly small and the mutual friction did not work effectively [1]. It is unclear how the vortices decay. Motivated by this experimental work, we studied numerically the vortex dynamics without the mutual friction, thus finding some cascade process which was obscured by the normal fluid at higher temperatures. This paper reviews our recent works on this problem. The numerical procedure based on the vortex filament formulation is described in detail in Ref. [2]. Section 2 describes the dynamics of waves excited along the reconnected vortex lines under the full Biot-Savart law and the energy spectrum characteristic of the cascade process [3]. Section 3 studies the dynamics of a dense vortex tangle(VT) by the calculation under the localized induction approximation(LIA) [2]. The absence of the mutual friction makes the vortices kinked, which promotes vortex reconnections. Consequently small vortices are cut off from a large one through the reconnections. The resulting vortices also follow the self-similar process to break up to smaller ones. Although our formulation cannot describe the final destiny of the minimum vortex, the decay of the VT is found to be connected with this cascade process, which is just the cascade process at zero temperature Feynman proposed [4]. It should be noted that this cascade process in a VT includes not only the breaking up of vortices but also the vortex wave process described in Sect. 2.