Comment on "Dynamics of the Density of Quantized Vortex-Lines in Superfluid Turbulence"

TL;DR

This paper critiques a previous numerical analysis of superfluid turbulence, arguing that their method for deriving the Vinen equation's production term is flawed and their conclusions are not definitive.

Contribution

It challenges the validity of prior methods used to determine the vortex line density dynamics in superfluid turbulence.

Findings

Questionable steps in velocity decomposition and flux interpretation.

Sensitivity of the Vinen equation shape to methodological choices.

Final conclusions of the original study are not unambiguous.

Abstract

In the paper by Khomenko et al. [Phys. Rev. B \textbf{91}, 180504 (2015)] the authors, analyzing numerically the steady counterflowing helium in inhomogeneous channel flow, concluded that the production term $\mathcal{P}$ in the Vinen equation is proportional to $\left\vert \mathbf{V}_{ns}\right\vert ^{3}\mathcal{L}^{1/2}$ (where $\mathcal{L}$ is vortex line density and $\mathbf{V}_{ns}$ is the counterflow velocity). In present comment we demonstrated that the procedure, implemented by the authors includes a number of questionable steps, such as a decomposition of velocity of line and interpretation of the flux term. Additionally, the overall strategy - extracting information on the temporal behavior from the stationary solution also remains questionable. Because of that the method of determination of the explicit shape of Vinen equation is very sensitive to the listed elements, the final conclusion of the authors cannot be considered as unambiguous.