Vortex coarsening in a superfluid shear layer

In classical 2D fluids, the end state of decaying turbulence often consists of multiple high circulation vortices, known as a vortex crystal [1, 2]. These quasi-equilibrium states contrast with the predictions of equilibrium statistical mechanics that instead predict a single highly-concentrated cluster [3]. In this work, we investigate decaying turbulence in a 2D quantum fluid and look for evidence of progressive vortex clustering [4]. Our initial state is a ring of closely-spaced quantized vortices, corresponding to a superfluid shear layer. The shear layer is unstable via an analogy to the classical Kelvin-Helmholtz instability [5].

After preparing the vortex ring we measure the vortex cluster number during the ensuing turbulence decay, utilizing a k-means clustering algorithm. We find analogous behaviour to decaying classical 2D turbulence, observing self-similar decay in the cluster number. This is characterized by a power-law dependence on time, with the number of vortex clusters varying as $N(t) \propto t^{-\alpha}$, where $\alpha =0.21\pm0.07$  . While our experiment is limited to a total vortex number of $N = 20$, we extend our numerical analysis to $N = 200 vortices$, finding that the exponent approaches $\alpha \approx 0.7$ independent of vortex number. Despite confirming self-similar decay, we find that the system does equilibrate to a single cluster instead of remaining in a vortex crystal state. For $t > 1$ s the state matches the predictions of maximum fluid entropy models, consisting of a single vortex cluster.

[1] D. Z. Jin and D. H. E. Dubin, Regional maximum entropy theory of vortex crystal formation, Phys. Rev. Lett. 80, 4434 (1998)

[2] P. Tabeling, Two-dimensional turbulence: a physicist approach, Physics Reports 362, 1 (2002).

[3] L. Onsager, Statistical hydrodynamics, Il Nuovo Cimento (1943-1954) 6, 279 (1949).

[4] S. Simjanovski et al., Shear-induced decaying turbulence in Bose-Einstein condensates (2024), arXiv:2408.02200 [cond-mat.quant-gas].

[5] D. Hernàndez-Rajkov et al., Connecting shear flow and vortex array instabilities in annular atomic superfluids, Nature Physics 20, 939 (2024).

 Numbers needed. I think you can do latex in the abstract submission — I’ve highlighted the stuff that needs $$ math mode around it.