Vortex Line Density Fluctuations of Quantum Turbulence

Fujiyama, Shoji; Tsubota, Makoto

doi:10.1007/s10909-009-9922-y

Cited by 5 publications

(8 citation statements)

References 16 publications

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“…The vortex length distribution is the probability density function of the existence of vortex rings in the tangle depending on their sizes. The distribution has been studied previously [31,32], especially with the expectation that it shows a self-similar structure. Fujiyama and Tsubota found that the distribution obeys a self-similar distribution and corresponds to the fluctuation of the vortex line density [32].…”

Section: Fractal Dimensionmentioning

confidence: 99%

“…The distribution has been studied previously [31,32], especially with the expectation that it shows a self-similar structure. Fujiyama and Tsubota found that the distribution obeys a self-similar distribution and corresponds to the fluctuation of the vortex line density [32]. In this study, we collect data on the lengths of rings and investigated the distribution and dependence on the anisotropy of the tangles.…”

Section: Fractal Dimensionmentioning

confidence: 99%

“…In this study, we have developed the previous study and investigated the internal structure of vortex tangles with the expectation of self-similarity. To accomplish this goal, we have studied the fractal dimension [29,30] and the vortex length distribution [31,32], which may reveal the selfsimilarity of vortex tangles directly: The fractal dimension is a noninteger dimension that characterizes a self-similar structure. This dimension was calculated by Kivotides et al for vortex tangles in periodic boundary conditions [30].…”

Section: Introductionmentioning

confidence: 99%

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Internal structure of localized quantized vortex tangles

2021

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In this study, we numerically investigate the internal structure of localized quantum turbulence in superfluid 4 He at zero temperature with the expectation of self-similarity in the real space. In our previous study, we collected the statistics of vortex rings emitted from a localized vortex tangle. As a result, the power law between the minimum size of detectable vortex rings and the emission frequency is obtained, which suggests that the vortex tangle has self-similarity in the real space [Nakagawa et al., Phys. Rev. B 101, 184515 (2020)]. In this work, we study the fractal dimension and vortex length distribution of localized vortex tangles, which can show their self-similar structure. We generate statistically steady and localized vortex tangles by injecting vortex rings with a fixed size. We used two types of injection methods that produce anisotropic or isotropic tangles. The injected vortex rings develop into a localized vortex tangle consisting of vortex rings of various sizes through reconnections (fusions and splitting of vortices). The fractal dimension is an increasing function of the vortex line density and becomes saturated to a value of approximately 1.8, as the density increases sufficiently. The behavior of the fractal dimension was independent of the anisotropy of the vortex tangles. The vortex length distribution indicates the number of vortex rings of each size that are distributed in a tangle. The distribution of the anisotropic vortex tangle shows the power law in the range above the injected vortex size, although the distribution of the isotropic vortex does not.

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Section: Fractal Dimensionmentioning

confidence: 99%

Section: Fractal Dimensionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Internal structure of localized quantized vortex tangles

2021

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show abstract

“…The vortex length distribution is the probability density function of the existence of vortex rings in the tangle depending on their sizes. The distribution has been studied previously [31,32], especially with the expectation that it shows a self-similar structure. Fujiyama et al found that the distribution obeys a self-similar distribution and corresponds to the fluctuation of the vortex line density [32].…”

Section: Vortex Length Distributionmentioning

confidence: 99%

“…In this study, we develop the previous study and investigated the internal structure of vortex tangles with the expectation of self-similarity. To accomplish this goal, we studied the fractal dimension [29,30] and the vortex length distribution [31,32], which can show the self-similarity of vortex tangles directly. The fractal dimension is a non-integer dimension that characterizes a self-similar structure.…”

Section: Introductionmentioning

confidence: 99%