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

TL;DR

This paper defends a new form of the vortex-line density evolution equation in superfluid turbulence, providing physical explanations and numerical validation for the proposed closure, addressing previous critiques.

Contribution

It offers a physical justification and numerical validation for the improved closure of the vortex-line density evolution equation in superfluid turbulence.

Findings

The new closure form aligns well with numerical results.

The flux term closure agrees with simulations without fitting parameters.

Provides a physical explanation for the improved model.

Abstract

This is a Reply to Nemirovskii Comment [Phys. Rev. B 94, 146501 (2016)] on the Khomenko et al, [Phys.Rev. B v.91, 180504(2016)], in which a new form of the production term in Vinen's equation for the evolution of the vortex-line density $\cal L$ in the thermal counterflow of superfluid $^4$He in a channel was suggested. To further substantiate the suggested form which was questioned in the Comment, we present a physical explanation for the improvement of the closure suggested in Khomenko et al [Phys.Rev. B v. 91, 180504(2016)] in comparison to the form proposed by Vinen. We also discuss the closure for the flux term, which agrees well with the numerical results without any fitting parameters.