Hideo Yano | Searcharxiv

arXiv2020

Statistical laws and self-similarity of vortex rings emitted from a localized vortex tangle in superfluid ${}^4$He

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.

cond-mat.other↗

arXiv2013

Statistics of vortex loops emitted from quantum turbulence driven by an oscillating sphere

We perform numerical simulation of quantum turbulence at zero temperature generated by an oscillating sphere. In this simulation, we injected vortices on the sphere to generate turbulence. Although we prepare injected vortex loops of identical length, they are extended by the oscillating sphere to form a tangle through numerous reconnections. The resulting tangle around the sphere is anisotropic and affected by the oscillation. The vortex tangle continues to emit vortex loops, which leave the sphere. The statistics of emitted loops differ significantly from those of the original injected vortices. First, the sizes of the emitted loops are widely distributed, ranging from smaller to much larger than the size of the initial injected loop. Second, the propagation direction of the emitted loops exhibits anisotropy: Small loops move away almost isotropically but large ones do so anisotropically along the oscillation direction of the sphere. Thus, the oscillating object stirs the initial injected vortices to reproduce a group of vortices with different statistics. Such physics is compared with the experiments of vibrating objects.

cond-mat.other↗