So the first paper I co-authored has now finally been published in Fluid Dynamics Research!
My contribution to this paper was based on a numerical code I wrote to compute a range of topological and geometrical properties of superfluid vortices, notably computing a knot invariant known as the Alexander polynomial.
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). We show that, at any instant, the turbulence consists of many unknots and few large loops of great geometrical and topological complexity.