论文标题
从超级流体$ {}^4 $ He中发出的局部涡流缠结发出的涡旋环的统计定律和自相似性
Statistical laws and self-similarity of vortex rings emitted from a localized vortex tangle in superfluid ${}^4$He
论文作者
论文摘要
我们在超级流体$^4 $中进行了数值模拟的量子湍流，以调查局部涡流缠结的涡流环的发射。湍流的特征是一些普遍的统计定律。尽管关于大量量子湍流的统计定律有很多研究，但对不均匀或局部湍流的研究很少。我们首先研究了局部量子湍流的统计定律，指的是[yano $ et $ et $al。$，J。LOW TEMP。物理。 $ \ bf {196} $，$ 184 \（2019）$]。第一定律是检测涡旋环的泊松过程。涡流缠结以频率散发出涡旋环，具体取决于它们的尺寸。第二定律是发射涡流环的频率和大小之间的权力定律，显示了缠结的自相似性。为了通过数值研究这些统计定律，我们开发了一个类似于实验的系统。首先，我们通过从两个相反的边注入涡旋环并导致碰撞来生成局部统计上稳定的涡旋缠结。我们研究了有助于形成缠结的形成的条件以及缠结环的发射的各向异性。其次，根据发射环的数据，我们重建了这两个统计定律。我们的数值研究结果与已知的涡旋环和局部缠结的已知自相似性一致。
We numerically simulated quantum turbulence in superfluid $^4$He to investigate the emission of vortex rings from a localized vortex tangle. Turbulence is characterized by some universal statistical laws. Although there are a lot of studies on statistical laws in bulk quantum turbulence, studies in inhomogeneous or localized turbulence is scarce. We first investigate the statistical laws of localized quantum turbulence, referring to two statistical laws deduced from the vibrating wire experiments in [Yano $et$ $al.$, J. Low Temp. Phys. $\bf{196}$, $184\ (2019)$]. The first law is the Poisson process for the detection of vortex rings; the vortex tangle emits vortex rings with frequencies depending on their sizes. The second law is the power law between the frequency and the size of the emitted vortex rings, showing the self-similarity of the tangle. To study these statistical laws numerically, we developed a system similar to experiments. First, we generate a localized statistically steady vortex tangle by injecting vortex rings from two opposite sides and causing collisions. We investigated the conditions that aid the formation of the tangles and the anisotropy of the emission of vortex rings from the tangle. Second, from the data on emitted rings, we reconstruct the two statistical laws. Results from our numerical investigations are consistent with the known self-similarity of emitted vortex rings and localized tangles.
