Helicity and topology of a small region of quantum vorticity

TL;DR

This paper investigates the dynamics, geometry, and topology of a small turbulent region of quantized vorticity in superfluid helium, revealing a fluctuating steady-state with complex knots and loops.

Contribution

It provides the first detailed numerical analysis of the topological and geometrical properties of quantum turbulence in superfluid helium.

Findings

Turbulence reaches a fluctuating steady-state in energy, geometry, and topology.

The knot spectrum shows many unknots and few large, complex loops.

Quantum turbulence exhibits rich topological structures similar to classical turbulence.

Abstract

We numerically study the evolution of a small turbulent region of quantised vorticity in superfluid helium, a regime which can be realised in the laboratory. We show that the turbulence achieves a fluctuating steady-state in terms of dynamics (energy), geometry (length, writhing) and topology (linking). After defining the knot spectrum, we show that, at any instant, the turbulence consists of many unknots and few large loops of great geometrical and topological complexity.