Nonlocal effects in superfluid turbulence: Application to the low-density- to high-density-state transition and to vortex decay

Abstract

We discuss a phenomenological equation for the evolution of vortex tangle in counterflow superfluid turbulence, which takes into account the influence of the nonlocal effects, introducing into the original equation of Vinen two simple corrective terms dependent on a nonvanishing ratio between the average separation between vortex lines and the diameter of the channel. The equation allows one to describe, in relatively good agreement with experimental results, the two turbulent regimes present in counterflow superfluid turbulence and the transition between them. The decay rate of the vortex line density $L$, when the heat flux is suddenly turned off, is also investigated; due to the simplicity of the model, which does not take into account the coupling of the line density $L$ with the superfluid velocity, this decay agrees with experiments in the initial and intermediate stages, but does not describe the full slow-down observed at very long times.