On the Nonuniform Quantum Turbulence in Superfluids

TL;DR

This paper refines the Vinen theory for quantum turbulence in superfluid helium by incorporating transverse vortex line density flux mechanisms, especially phase slippage, to better describe inhomogeneous and nonstationary turbulence.

Contribution

It introduces a modified Vinen equation including transverse flux effects, notably phase slippage, improving the modeling of inhomogeneous quantum turbulence.

Findings

Inclusion of transverse flux mechanisms improves VLD distribution modeling.

Phase slippage is identified as the most effective flux mechanism.

The modernized Vinen equation accurately describes stationary and nonstationary turbulence.

Abstract

The problem of quantum turbulence in a channel with an inhomogeneous counterflow of superfluid turbulent helium is studied. \ The counterflow velocity $V_{ns}^{x}(y)$ along the channel is supposed to have a parabolic profile in the transverse direction $y$. Such statement corresponds to the recent numerical simulation by Khomenko et al. [Phys. Rev. B \textbf{91}, 180504 (2015)]. The authors reported about a sophisticated behavior of the vortex line density (VLD) $\mathcal{L}(\mathbf{r},t)$, different from $% \mathcal{L}\propto V_{ns}^{x}(y)^{2}$, which follows from the naive, straightforward application of the conventional Vinen theory. It is clear, that Vinen theory should be refined by taking into account transverse effects and the way it ought to be done is the subject of active discussion in the literature. In the work we discuss several possible mechanisms of the transverse flux of VLD $\mathcal{L}(\mathbf{r},t)$ which should be incorporated in the standard Vinen equation to describe adequately the inhomogeneous quantum turbulence (QT). It is shown that the most effective among these mechanisms is the one that is related to the phase slippage phenomenon. The use of this flux in the modernized Vinen equation corrects the situation with an unusual distribution of the vortex line density, and satisfactory describes the behavior $\mathcal{L}(\mathbf{r},t)$ both in stationary and nonstationary situations. The general problem of the phenomenological Vinen theory in the case of nonuniform and nonstationary quantum turbulence is thoroughly discussed.