Local and nonlocal dynamics in superfluid turbulence

TL;DR

This paper investigates the differences in energy spectra and vortex interactions in superfluid turbulence, distinguishing between Kolmogorov and Vinen tangles based on local and nonlocal vortex dynamics.

Contribution

It identifies spectral signatures of two turbulence types and analyzes how local versus nonlocal vortex interactions influence their structures.

Findings

Vinen tangles depend mainly on local vortex curvature.

Kolmogorov tangles exhibit dominant long-range vortex interactions.

Clustering of vortex lines occurs in Kolmogorov turbulence.

Abstract

Turbulence in superfluid helium~II is a tangle of quantized vortex lines which interact via the classical Biot-Savart law. We show that vortex tangles with the same vortex line density will have different energy spectra, depending on the normal fluid which feeds energy into the superfluid component, and identify the spectral signature of two forms of superfluid turbulence: Kolmogorov tangles and Vinen tangles. By decomposing the superfluid velocity field into local and nonlocal contributions, we find that in Vinen tangles the motion of vortex lines depends mainly on the local curvature, whereas in Kolmogorov tangles the long-range vortex interaction is dominant and leads to the formation of clustering of lines, in analogy to the 'worms` of ordinary turbulence.