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 loops, 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 intervortex 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. In particular, we observe the emergence of the power-law scalings predicted by 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, these findings are 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. This work paves the way for an interpretation of inertial-range dynamics in terms of the polarization and spatial arrangement of vortex filaments.

中文翻译：

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量子湍流中速度循环的间歇性

速度循环是封闭路径内流体旋转的量度，是经典流和量子流中的基本观测结果。实际上，它是无粘性经典流体中的拉格朗日不变式。在量子流中，通过离散值来量化循环，离散值与路径所包围的细涡旋丝的数量和方向直接相关。通过改变这种闭环的大小，循环提供了流动结构对所考虑规模的依赖性的量度。在这里，我们使用广义Gross-Pitaevskii模型的高分辨率直接数值模拟来考虑量子湍流中循环统计量的尺度依赖性。将结果与通过不可压缩的Navier-Stokes方程的模拟获得的循环统计数据进行比较。当积分路径小于平均涡旋距离时，由于湍流的量化，量子湍流中的循环统计数据显示出极端的间歇行为，这与经典流的粘性尺度形成了鲜明的对比。相反，在更大的尺度上，环流矩与经典湍流惯性范围内的统计数据显示出惊人的相似性。特别是，我们观察到了由Kolmogorov的1941年理论所预测的幂律定标的出现，以及间歇性偏差，这些偏差紧密地遵循了最近提出的经典流中转弯矩的双分形模型。迄今为止，这些发现是大规模湍流中最令人信服的间歇性证据。而且，先验的系统非常不同。这项工作为根据涡旋丝的极化和空间排列解释惯性范围动力学铺平了道路。