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arXiv 1202.0579physics.flu-dyncond-mat.quant-gascond-mat.stat-mech
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量子Turbulence中尺度动能均分

Mesoscale Equipartition of kinetic energy in Quantum Turbulence

Julien Salort, Philippe-E. Roche, Emmanuel Lévêque

摘要:

对有限温度下超流氦的湍流进行了数值研究。直接数值模拟进行了“截断HVBK”模型,它结合了连续描述的Hall-Vinen-Bekeravich-Khalatnikov方程的附加约束,这种连续的描述不能超出量子长度尺度与个人超流涡之间的平均间距。一个很好的协议被发现与实验测量的旋涡密度。此外,通过改变湍流强度,观察到涡间距随雷诺数的变化规律为$Re^{-3/4}$,与经典湍流中的粘性尺度相似。在高温极限,Kolmogorov的惯性叶栅恢复,从以前的数值和实验研究的预期。随着温度的降低,惯性级联仍然存在于大尺度,而在小尺度下,该系统的发展对统计均分的动能之间的频谱模式,与特征$k^2$速度谱。超流激发在一系列介观尺度上的积累使超流能够通过与剩余的正常流体的相互摩擦来持续耗散动能,尽管后者在低温下变得罕见。结果表明,在低温下,超流涡量主要集中在这些中尺度区域,而在高温下,超流涡量主要集中在惯性区域。这一观察结果应对衰减湍流实验的解释产生影响,这些实验通常基于涡线密度测量。

英文摘要:

The turbulence of superfluid helium is investigated numerically at finite temperature. Direct numerical simulations are performed with a "truncated HVBK" model, which combines the continuous description of the Hall-Vinen-Bekeravich-Khalatnikov equations with the additional constraint that this continuous description cannot extend beyond a quantum length scale associated with the mean spacing between individual superfluid vortices. A good agreement is found with experimental measurements of the vortex density. Besides, by varying the turbulence intensity only, it is observed that the inter-vortex spacing varies with the Reynolds number as $Re^{-3/4}$, like the viscous length scale in classical turbulence. In the high temperature limit, Kolmogorov's inertial cascade is recovered, as expected from previous numerical and experimental studies. As the temperature decreases, the inertial cascade remains present at large scales while, at small scales, the system evolves towards a statistical equipartition of kinetic energy among spectral modes, with a characteristic $k^2$ velocity spectrum. The accumulation of superfluid excitations on a range of mesoscales enables the superfluid to keep dissipating kinetic energy through mutual friction with the residual normal fluid, although the later becomes rare at low temperature. It is found that most of the superfluid vorticity can concentrate on these mesoscales at low temperature, while it is concentrated in the inertial range at higher temperature. This observation should have consequences on the interpretation of decaying turbulence experiments, which are often based on vortex line density measurements.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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