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

In the paper by Khomenko et al. [Phys. Rev. B $\mathbf{\text{91}}$, 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$$\mathcal{L}$$isvortexlinedensityand$$\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.