Abstract
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 quantized, 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 generalized 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 behavior due to the quantization 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 resemblance between classical and quantum turbulence, highlighting the universality of inertial range dynamics, including intermittency, across these two a priori very different systems.
Highlights
The motion of vortices in fluid flows, including rivers, tornadoes, and the outer atmosphere of planets like Jupiter, has fascinated observers for centuries
The recent work of Iyer et al [20] has sparked renewed interest in the statistics of velocity circulation in highReynolds-number classical turbulent flows. Their numerical results have showcased the relative simplicity of circulation statistics in the inertial range, despite the intermittency of these flows
This simplicity contrasts with the complexity of velocity increment statistics, as well as that of enstrophy or dissipation, which display multifractal statistics as a result of turbulence intermittency [14]
Summary
The motion of vortices in fluid flows, including rivers, tornadoes, and the outer atmosphere of planets like Jupiter, has fascinated observers for centuries. [32] to show that, in quantum turbulence, the intermittency of velocity increments is enhanced with respect to classical turbulence Note that such decomposition is not needed for circulation statistics since the compressible components of the velocity are, by definition, potential flows [29], and their contributions to the circulation vanish when evaluating the contour integral in Eq (1). This absence of ambiguity, as well as its discrete nature, makes the circulation a interesting quantity to study in low-temperature quantum turbulence.
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