Title: Scaling properties of velocity circulation in classical and quantum turbulence

Contact: Nicolas Mordant (Ã‰quipe EDT)

Abstract: The velocity circulation, a measure of the rotation of a fluid within a closed path, is a fundamental observable in fluid flows. By varying the size of such closed loops, the circulation can provide a measure of the dependence of the flow structure on the considered scale. Such circulation-based diagnostics may therefore provide important information on the complex spatio-temporally intermittent structure of turbulent flows. It has recently been shown numerically that this is indeed the case in classical fluids, as this intermittency phenomenon appears to have a relatively simple signature on circulation statistics.

In contrast to classical fluids, the circulation in low-temperature quantum fluids (such as superfluid helium or Bose-Einstein condensates) is quantised, taking discrete values that are directly related to the number and the orientation of thin vortex filaments enclosed by the chosen path. At macroscopic scales, it has been observed that the complex dynamics of such discrete vortices can exhibit a turbulent state not unlike classical flows, including the emergence of Kolmogorov’s K41 scaling laws.

Here, using high-resolution direct numerical simulations of classical turbulence and low-temperature quantum turbulence, we show that the similarities between both systems go far beyond self-similar K41 theory. Indeed, the circulation in quantum turbulence displays intermittency deviations from K41 predictions which closely follow those observed in classical flows. Our results strongly reinforce the resemblance between these a priori very different systems, putting forward the idea of using quantum flows as a tool to improve our understanding of classical turbulence. Based on this idea, we finally suggest a possible path towards an interpretation of inertial-range turbulence dynamics in terms of the polarisation and the spatial arrangement of discrete vortex filaments, such as those naturally observed in quantum fluids.