Polanco Juan Ignacio, Roche Philippe-E, Danaila Luminita, Lévêque Emmanuel
CNRS, Ecole Centrale de Lyon, Institut National des Sciences Appliquées de Lyon, Universite Claude Bernard Lyon 1, Laboratoire de Mécanique des Fluides et d'Acoustique, UMR 5509, Ecully 69130, France.
Université Grenoble Alpes, CNRS, Institut National Polytechnique de Grenoble, Laboratoire des Ecoulements Géophysiques et Industriels, Grenoble 38000, France.
Proc Natl Acad Sci U S A. 2025 Jul 8;122(27):e2426598122. doi: 10.1073/pnas.2426598122. Epub 2025 Jul 3.
The interplay between viscous and frictional dissipation is key to understanding quantum turbulence dynamics in superfluid He. Based on a coarse-grained two-fluid description, an original scale-by-scale energy budget that identifies each scale's contribution to energy dissipation is derived. Using the Hall-Vinen-Bekharevich-Khalatnikov (HVBK) model to further characterize mutual friction, direct numerical simulations at temperatures 1.44 K ≲ ≲ 2.16 K indicate that mutual friction promotes intense momentum exchanges between the two fluids to maintain a joint energy cascade despite their viscosity mismatch. However, the resulting overall frictional dissipation remains small (compared to the viscous dissipation) and confined to far-dissipative scales. This remarkable feature allows us to define an effective Reynolds number for the turbulence intensity in a two-fluid system, helping to disentangle the effects of Reynolds number and temperature in quantum turbulence. Thereby, simple physical arguments predict that the distance between quantized vortices (normalized by the turbulence integral scale ) should behave as [Formula: see text] with the Reynolds number based on the quantum of circulation . This law is well supported by a large set of experimental and numerical data within the temperature range of the HVBK model. Finally, this approach offers the possibility of revisiting the ongoing controversy on intermittency in quantum turbulence. It is shown that observed changes in intermittency arise from Reynolds number effects rather than from temperature variations, as proposed in recent studies.
粘性耗散与摩擦耗散之间的相互作用是理解超流氦中量子湍流动力学的关键。基于粗粒化双流体描述，推导了一种原始的逐尺度能量收支，该收支确定了每个尺度对能量耗散的贡献。使用霍尔 - 维宁 - 贝哈列维奇 - 哈拉特尼科夫（HVBK）模型进一步表征相互摩擦，在1.44K≲ ≲2.16K温度下的直接数值模拟表明，尽管两种流体的粘度不匹配，但相互摩擦促进了两种流体之间强烈的动量交换，以维持联合能量级串。然而，由此产生的总摩擦耗散仍然很小（与粘性耗散相比），并且局限于远耗散尺度。这一显著特征使我们能够为双流体系统中的湍流强度定义一个有效雷诺数，有助于厘清雷诺数和温度在量子湍流中的影响。因此，简单的物理论证预测，量子化涡旋之间的距离（由湍流积分尺度归一化）应与基于环流量子的雷诺数满足[公式：见原文]。在HVBK模型的温度范围内，大量的实验和数值数据很好地支持了这一定律。最后，这种方法为重新审视关于量子湍流间歇性的持续争议提供了可能性。结果表明，观察到的间歇性变化源于雷诺数效应，而不是如最近研究所提出的温度变化。
