Symmetry of Kelvin-wave dynamics and the Kelvin-wave cascade in the T=0 superfluid turbulence

TL;DR

This paper explores the symmetry properties of Kelvin-wave dynamics in superfluid turbulence, demonstrating that tilt symmetry is preserved in the cascade process despite non-invariant spectra, and proposes a simplified crossover model.

Contribution

It clarifies the role of tilt symmetry in Kelvin-wave cascades and introduces a straightforward crossover picture from classical to quantum turbulence.

Findings

Kelvin-wave spectrum is not tilt-invariant.

Tilt invariance of the Kelvin-wave cascade is maintained.

A simple crossover model avoids energy mismatch issues.

Abstract

The article considers implications of tilt symmetry (symmetry with respect to tilting of the coordinate axis with respect to which vortex motion is studied) in the non-linear dynamics of Kelvin waves. The conclusion is that although the spectrum of Kelvin wave is not tilt-invariant, this does not compromise tilt invariance of the Kelvin-wave cascade vividly argued now in the theory of superfluid turbulence. The article investigates the effect of strong kelvon interaction on the power-law exponent for the Kelvin-wave cascade and suggests a simple picture of the crossover from the classical Kolmogorov cascade to the quantum Kelvin-wave cascade, which does not encounter with mismatch of the energy distributions at the crossover and does not require a broad intermediate interval for realization of the crossover.