Reply to Comment on "Symmetry of Kelvin-wave dynamics and the Kelvin-wave cascade in the T=0 superfluid turbulence" [arXiv:1208.4593]

TL;DR

This paper is a detailed response to a comment by L'vov and Nazarenko, defending previous criticisms of their Kelvin-wave cascade mechanism and highlighting issues related to tilt invariance in their Hamiltonian.

Contribution

The paper clarifies the implications of tilt invariance violations in the Hamiltonian used for Kelvin-wave cascade models, reinforcing the author's prior critique.

Findings

L'vov and Nazarenko's Hamiltonian is not tilt-invariant.

Violation of tilt symmetry challenges their cascade mechanism.

The author's critique remains valid based on symmetry considerations.

Abstract

I discuss the Comment by L'vov and Nazarenko (arXiv:1208.4593) aiming at refutation of my perviously published criticism of their mechanism of the Kelvin-wave cascade. It is important that in their Comment L'vov and Nazarenko admitted that the Hamiltonian, from which they derived their mechanism, is not tilt-invariant. This provides full ammunition to their critics, who believe that their mechanism is in conflict with tilt symmetry of the Kelvin-wave dynamics in an isotropic space.