arXiv subjects

Hiromichi Kobayashi

Publications and source records attributed to Hiromichi Kobayashi.

11 recordsLinked to original sources

arXiv2024

Influence of different mutual friction models on two-way coupled quantized vortices and normal fluid in superfluid $^4$He

We study the influence of two mutual friction models on quantized vortices and normal fluid using two-way coupled simulations of superfluid $^4$He. The normal fluid is affected by quantized vortices via mutual friction. A previous study [Y. Tang, et al. Nat. Commun. 14, 2941 (2023)] compared the time evolutions of the vortex ring radius and determined that the self-consistent two-way coupled mutual friction (S2W) model yielded better agreement with the experimental results than the two-way coupled mutual friction (2W) model whose model parameters were determined through experiments with rotating superfluid helium. In this study, we compare the two models in more detail in terms of the quantized vortex ring propagation, reconnection, and thermal counterflow. We show that the S2W model exhibits better results than the 2W model on the microscopic scale near a quantized vortex, such as during quantized vortex ring propagation and reconnection, although the S2W model requires a higher spatial resolution. For complex flows such as a thermal counterflow, the 2W model can be applied even to a low-resolution flow while maintaining the anisotropic normal fluid velocity fluctuations. In contrast, the 2W model predicts lower normal fluid velocity fluctuations than the S2W model. The two models show probability density functions with $- 3$ power-law tails for the normal fluid velocity fluctuations.

cond-mat.other↗

arXiv2023

Analysis of anisotropic subgrid-scale stress for coarse large-eddy simulation

This study discusses the necessity of anisotropic subgrid-scale (SGS) stress in large-eddy simulations (LESs) of turbulent shear flows using a coarse grid resolution. We decompose the SGS stress into two parts to observe the role of SGS stress in turbulent shear flows in addition to the energy transfer between grid-scale (GS or resolved scale) and SGS. One is the isotropic eddy-viscosity term, which contributes to energy transfer, and the other is the residual anisotropic term, which is separated from the energy transfer. We investigate the budget equation for GS Reynolds stress in turbulent channel flows accompanied by the SGS stress decomposition. In addition, we examine the medium and coarse filter length cases; the conventional eddy-viscosity models can fairly predict the mean velocity profile for the medium filter case and fails for the coarse filter case. The budget for GS turbulent kinetic energy shows that the anisotropic SGS stress has a negligible contribution to energy transfer. In contrast, the anisotropic stress has a large and non-dissipative contribution to the streamwise and spanwise components of GS Reynolds stress when the filter size is large. Even for the medium-size filter case, the anisotropic stress contributes positively to the budget for the spanwise GS Reynolds stress. Spectral analysis of the budget reveals that the positive contribution is prominent at a scale consistent with the spacing of streaks in the near-wall region. Therefore, we infer that anisotropic stress contributes to the generation mechanism of coherent structures. Predicting the positive contribution of the anisotropic stress to the budget is key to further improving SGS models.

physics.flu-dyn↗

arXiv2022

Imaging the decay of quantized vortex rings to decipher quantum dissipation

Like many quantum fluids, superfluid helium-4 (He II) can be considered as a mixture of two miscible fluid components: an inviscid superfluid and a viscous normal fluid consisting of thermal quasiparticles [1]. A mutual friction between the two fluids can emerge due to quasiparticles scattering off quantized vortex lines in the superfluid [2]. This quantum dissipation mechanism is the key for understanding various fascinating behaviors of the two-fluid system [3,4]. However, due to the lack of experimental data for guidance, modeling the mutual friction between individual vortices and the normal fluid remains an unsettled topic despite decades of research [5-10]. Here we report an experiment where we visualize the motion of quantized vortex rings in He II by decorating them with solidified deuterium tracer particles. By examining how the rings spontaneously shrink and accelerate, we provide unequivocal evidences showing that only a recent theory [9] which accounts for the coupled motion of the two fluids with a self-consistent local friction can reproduce the observed ring dynamics. Our work eliminates long-standing ambiguities in our theoretical description of the vortex dynamics in He II, which will have a far-reaching impact since similar mutual friction concept has been adopted for a wide variety of quantum two-fluid systems, including atomic Bose-Einstein condensates (BECs) [11,12], superfluid neutron stars [13-15], and gravity-mapped holographic superfluid [16,17].

cond-mat.quant-gas↗

arXiv2022

Transport and modeling of subgrid-scale turbulent kinetic energy in channel flows

To develop a more convenient subgrid-scale (SGS) model that performs well even in coarse grid cases, we investigate the transport and modeling of SGS turbulent kinetic energy (hereafter SGS energy) in turbulent channel flows based on the stabilized mixed model (SMM). In this paper, we try to increase the convenience of the SMM by replacing the modeled transport equation for the SGS energy with an algebraic model. The SMM quantitatively adequately predicts the total turbulent kinetic energy of the direct numerical simulation (DNS) even in coarse grid cases. For both the filtered DNS (fDNS) and large-eddy simulation (LES), the statistically averaged production term balances with the dissipation in the region away from the wall in the SGS energy transport equation. In contrast, we reveal that the correlation coefficient between the production and dissipation terms is high for the modeled transport equation in LES, whereas that for the fDNS is low. Based on the high correlation or local equilibrium between the production and dissipation observed in the LES, we demonstrate the reduction of the SMM into a zero-equation SMM (ZE-SMM). We construct a new damping function based on the grid-scale Kolmogorov length to reproduce the near-wall behavior of the algebraic model for the SGS energy. The ZE-SMM provides quantitatively the same performance as the original SMM that employs the SGS energy transport model. This result suggests that the local equilibrium model for the SGS energy provides the equivalent performance as the transport model in wall-bounded turbulent flows even in coarse grid cases.

physics.flu-dyn↗

arXiv2022

Universal anomalous turbulent diffusion in quantum fluids

In classical viscous fluids, turbulent eddies are known to be responsible for the rapid spreading of embedded particles. But in an inviscid quantum fluid where the turbulence is induced by a chaotic tangle of quantized vortices, dispersion of the particles is achieved via a non-classical mechanism, i.e., their binding to the evolving quantized vortices. However, there is limited existing knowledge on how the vortices diffuse and spread in turbulent quantum fluids. Here we report a systematic numerical study of the apparent diffusion of vortices in a random vortex tangle in superfluid helium-4 using full Biot-Savart simulation. We reveal that the vortices in pure superfluid exhibit a universal anomalous diffusion (superdiffusion) at small times, which transits to normal diffusion at large times. This behavior is found to be caused by a generic scaling property of the vortex velocity, which should exist in all quantum fluids where the Biot-Savart law governs the vortex motion. Our simulation at finite temperatures also nicely reproduces recent experimental observations. The knowledge obtained from this study may form the foundation for understanding turbulent transport and universal vortex dynamics in various condensed-matter and cosmic quantum fluids.

physics.flu-dyn↗

arXiv2021

Quantum Turbulence Coupled with Externally Driven Normal-Fluid Turbulence in Superfluid $^4$He

The coupled dynamics of quantum turbulence (QT) and normal-fluid turbulence (NFT) have been a central challenge in quantum hydrodynamics, since it is expected to cause the unsolved T2 state of QT. We numerically studied the coupled dynamics of the two turbulences in thermal counterflow. NFT is driven by external forces to control its turbulent intensity, and the fast multipole method accelerates the calculation of QT. We show that NFT enhances QT via mutual friction. The vortex line density $L$ of the QT satisfies the statistical law $L^{1/2} \approx γV_{ns}$ with the counterflow velocity $V_{ns}$. The obtained $γ$ agrees with the experiment of T2 state, validating the idea that the T2 state is caused by NFT. We propose a theoretical insight into the relation between the two turbulences.

cond-mat.supr-con↗

arXiv2020

Role of various scale-similarity models in stabilized mixed subgrid-scale model

We investigate the physical role of various scale-similarity models in the stabilized mixed model [K. Abe, Int. J. Heat Fluid Flow, 39, 42 (2013); M. Inagaki and K. Abe, Int. J. Heat Fluid Flow, 64, 137 (2017)] and evaluate their performance in turbulent channel flows. Among various models in the present study, the original model combined with the scale-similarity model for the subgrid-scale (SGS)-Reynolds term yields the best prediction for the anisotropy of the grid-scale (GS) velocity fluctuations and the SGS stress, even in coarse grid resolutions. Moreover, it successfully predicts large intensities of the spectra close to the cut-off scale in accordance with the filtered direct numerical simulation, whereas other models predict a rapid decay of the spectra in the low-wavelength region. To investigate the behavior of the models close to the cut-off scale, we analyze the budget equation for the GS Reynolds stress spectrum. The result shows that the scale-similarity model for the SGS-Reynolds term plays a role in the enhancement of the wall-normal velocity fluctuation close to the cut-off scale. Thereby, it activates turbulence close to the cut-off scale, leading to a reproduction of the proper streak structures observed in wall-bounded turbulent flows. The reproduction of velocity fluctuations close to the cut-off scale and turbulent structures is a key element for further development of SGS models.

physics.flu-dyn↗

arXiv2020

Fully Coupled Two-Fluid Dynamics in Superfluid $^4$He: Anomalous Anisotropic Velocity Fluctuations in Counterflow

We investigate the thermal counterflow of the superfluid $^4$He by numerically simulating three-dimensional fully coupled dynamics of the two fluids, namely quantized vortices and a normal fluid. We analyze the velocity fluctuations of the laminar normal fluid arising from the mutual friction with the quantum turbulence of the superfluid component. The streamwise fluctuations exhibit higher intensity and longer-range autocorrelation, as compared to transverse ones. The anomalous fluctuations are consistent with visualization experiments [Mastracci et al., Phys. Rev. Fluids, Vol. 4, 083305 (2019)], and our results confirm their analysis with simple models on the anisotropic fluctuations. This success validates the model of the fully coupled dynamics and paves the way for solving some outstanding problems in this two-fluid system.

cond-mat.supr-con↗

arXiv2019

Numerical Study on Entrance Length in Thermal Counterflow of Superfluid $^4$He

Three-dimensional numerical simulations in a square duct were conducted to investigate entrance lengths of normal fluid and superfluid flows in a thermal counterflow of superfluid $^4$He. The two fluids were coarse-grained by using the Hall-Vinen-Bekharevich-Khalatnikov (HVBK) model and were coupled through mutual friction. We solved the HVBK equations by parameterizing the coefficient of the mutual friction to consider the vortex line density. A uniform mutual friction parameter was assumed in the streamwise direction. Our simulation showed that the entrance length of the normal fluid from a hot end becomes shorter than that of a single normal fluid due to the mutual friction with the parabolically developed superfluid flow near the hot end. As the mutual friction increases, the entrance length decreases. Same as that, the entrance length of the superfluid from a cold end is affected by the strength of the mutual friction due to the parabolically developed normal fluid flow near the cold end. Aside from the entrance effect, the realized condition of a tail-flattened flow is discussed by parameterizing the superfluid turbulent eddy viscosity and the mutual friction.

cond-mat.other↗

arXiv2018

Three-Dimensional Coupled Dynamics of Two-Fluid Model in Superfluid $^4$He: Deformed Velocity Profile of Normal Fluid in Thermal Counterflow

The coupled dynamics of the two-fluid model of superfluid $^4$He is numerically studied for quantum turbulence of the thermal counterflow in a square channel. We combine the vortex filament model of the superfluid and the Navier-Stokes equations of normal fluid. Simulations of the coupled dynamics show that the velocity profile of the normal fluid is deformed significantly by superfluid turbulence as the vortices become dense. This result is consistent with recently performed visualization experiments. We introduce a dimensionless parameter that characterizes the deformation of the velocity profile.

cond-mat.other↗

arXiv2013

A Reynolds-averaged turbulence modeling approach to the maintenance of the Venus superrotation

A maintenance mechanism of an approximately linear velocity profile of the Venus zonal flow or superrotation is explored, with the aid of a Reynolds-averaged turbulence modeling approach. The basic framework is similar to that of Gierasch (1975) in the sense that the mechanism is examined under a given meridional circulation. The profile mimicking the observations of the flow is initially assumed, and its maintenance mechanism in the presence of turbulence effects is investigated from a viewpoint of the suppression of energy cascade. In the present work, the turbulent viscosity is regarded as an indicator of the intensity of the cascade. A novelty of this formalism is the use of the isotropic turbulent viscosity based on a nonlocal time scale linked to a large-scale flow structure. The mechanism is first discussed qualitatively. On the basis of these discussions, the two-dimensional numerical simulation of the proposed model is performed, with an initially assumed superrotation, and the fast zonal flow is shown to be maintained, compared with the turbulent viscosity lacking the nonlocal time scale. The relationship of the present model with the current general-circulation-model simulation is discussed in light of a crucial role of the vertical viscosity.

astro-ph.EP↗