Scanning Superfluid-Turbulence Cascade by Its Low-Temperature Cutoff

TL;DR

This paper develops a theory for the low-temperature cutoff in superfluid turbulence, linking vortex line density behavior to cascade structure, and validates it with recent experimental data, enhancing understanding of Kelvin-wave cascades.

Contribution

It introduces a theoretical model for the low-temperature cutoff in superfluid turbulence and confirms it through experimental validation, clarifying cascade behavior at ultra-low temperatures.

Findings

The theory predicts a specific behavior of vortex line density controlled by friction.

The ln L versus ln α curve reflects cascade structure with four distinct regions.

Experimental data agrees with the theory, validating the superfluid turbulence scenario.

Abstract

On the basis of recently proposed scenario of the transformation of the Kolmogorov cascade into the Kelvin-wave cascade, we develop a theory of low-temperature cutoff. The theory predicts a specific behavior of the quantized vortex line density, $L$, controlled by the frictional coefficient, $\alpha(T) \ll 1$, responsible for the cutoff. The curve $\ln L(\ln \alpha)$ is found to directly reflect the structure of the cascade, revealing four qualitatively distinct wavenumber regions. Excellent agreement with recent experiment by Walmsley {\it et al.} [arXiv:0710.1033]--in which $L(T)$ has been measured down to $T \sim 0.08 $K--implies that the scenario of low-temperature superfluid turbulence is now experimentally validated, and allows to quantify the Kelvin-wave cascade spectrum.