Reply to "Comment on 'Theoretical analysis of quantum turbulence using the Onsager ideal turbulence theory'"

TL;DR

This paper defends a previous theoretical analysis of quantum turbulence against criticism, clarifying key assumptions and proposing a refined analysis to support the original double-cascade scenario involving quantum and Richardson cascades.

Contribution

It refutes criticism of the original paper, clarifies circulation quantization, and introduces a more sophisticated analysis to uphold the double-cascade prediction in quantum turbulence.

Findings

Confirmation of the double-cascade scenario in quantum turbulence.

Refutation of the criticism regarding circulation quantization.

Proposal of a conjecture linking Kelvin-wave and quantum stress cascades.

Abstract

We refute the criticism expressed in a Comment by Krstulovic, L'vov, and Nazarenko [arXiv:2107.10598] on our paper [Phys. Rev. E 103, 023106 (2021)]. We first show that quantization of circulation is not ignored in our analysis. Then, we propose a more sophisticated analysis to avoid a subtle problem with the regularity of the velocity field. We thus defend the main results of our paper, which predicts the double-cascade scenario where the quantum stress cascade follows the Richardson cascade. We also provide a conjecture on the relation between the Kelvin-wave cascade and the quantum stress cascade.