Helicity and topology of a small region of quantum vorticity

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.