The velocity circulation, a measure of the rotation of a fluid within a closed path, is a fundamental observable in classical and quantum flows. It is indeed a Lagrangian invariant in inviscid classical fluids. In quantum flows, circulation is quantised, taking discrete values that are directly related to the number and the orientation of thin vortex filaments enclosed by the path. By varying the size of such closed loop, the circulation provides a measure of the dependence of the flow structure on the considered scale.
Here, we consider the scale dependence of circulation statistics in quantum turbulence, using high resolution direct numerical simulations of a generalised Gross–Pitaevskii model. Results are compared to the circulation statistics obtained from simulations of the incompressible Navier–Stokes equations. When the integration path is smaller than the mean inter-vortex distance, the statistics of circulation in quantum turbulence displays extreme intermittent behaviour due to the quantisation of circulation, in stark contrast with the viscous scales of classical flows. In contrast, at larger scales, circulation moments display striking similarities with the statistics probed in the inertial range of classical turbulence. This includes the emergence of the power law scalings predicted from Kolmogorov’s 1941 theory, as well as intermittency deviations that closely follow the recently proposed bifractal model for circulation moments in classical flows.
To date, this is the most convincing evidence of intermittency in the large scales of quantum turbulence. Moreover, our results strongly reinforce the analogy between classical and quantum turbulence, highlighting the universality of inertial range dynamics, including intermittency, across these two a priori very different systems. This work paves the way for an interpretation of inertial range dynamics in terms of the polarisation and spatial arrangement of vortex filaments.