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物性研究

Energy spectrum of superfluid turbulence : Numerical Analysis of the Gross-Pitaevskii equation with the small scale dissipation(3) Chaos and nonlinear dynamics in dissipative systems(including BEC and pattern formations), Chaos and Nonlinear Dynamics in Quantum-Mechanical and Macroscopic Systems)

Michikazu Kobayashi, Makoto Tsubota

Published Jun 20, 2005• 0 citations
OpenAlex

Abstract

We investigated dynamics of superfluid turbulence by the Gross-Pitaevskii equation and its relation to conventional classical turbulence. We introduced the dissipation term which is effective only in the scale smaller than the core size of quantized vortices, and found that the energy spectrum of superfluid turbulence was consistent with the Kolmogorov law which is one of the most important statistical laws of classical turbulence.

Related papers

Kolmogorov Spectrum of Superfluid Turbulence: Numerical Analysis of the Gross-Pitaevskii Equation with a Small-Scale Dissipation

Michikazu Kobayashi, Makoto Tsubota

The energy spectrum of superfluid turbulence is studied numerically by solving the Gross-Pitaevskii equation. We introduce the dissipation term which works only in the scale smaller than the healing length to remove short wavelength excitations which may hinder the cascade process of quantized vortices in the inertial range. The obtained energy spectrum is consistent with the Kolmogorov law.

arXiv:cond-mat/0411750•Physical Review Letters•Feb 14, 2005•223 citations

Kolmogorov Spectrum of Quantum Turbulence

Michikazu Kobayashi, Makoto Tsubota

There is a growing interest in the relation between classical turbulence and quantum turbulence. Classical turbulence arises from complicated dynamics of eddies in a classical fluid. In contrast, quantum turbulence consists of a tangle of stable topological defects called quantized vortices, and thus quantum turbulence provides a simpler prototype of turbulence than classical turbulence. In this paper, we investigate the dynamics and statistics of quantized vortices in quantum turbulence by numerically solving a modified Gross-Pitaevskii equation. First, to make decaying turbulence, we introduce a dissipation term that works only at scales below the healing length. Second, to obtain steady turbulence through the balance between injection and decay, we add energy injection at large scales. The energy spectrum is quantitatively consistent with the Kolmogorov law in both decaying and steady turbulence. Consequently, this is the first study that confirms the inertial range of quantum turbulence.

arXiv:cond-mat/0508624•Journal of the Physical Society of Japan•Dec 1, 2005•95 citations

Large Scale Numerical Simulation for Superfluid Turbulence

Narimasa Sasa, Masahiko Machida

Large scale numerical simulation of quantum turbulence is performed by using 3-D time-dependent Gross-Pitaevskii equation.The energy spectrum obeying Kolmogorov law and large scale self-similar structure of quantum vortex tangle are found in a fully developed dumped turbulent state.Width of the inertial range becomes large depending on the system size of the simulation that is consistent with the result of the normal fluid turbulence.On the other hand, bottleneck effect near coherent length prevents the inertial range from extending to smaller scale.

Progress in Nuclear Science and Technology•Oct 1, 2011•2 citations

SUPERFLUID TURBULENCE AND DYNAMICS OF QUANTIZED VORTICES

Makoto Tsubota

Superfluid turbulence has been one of the most important problems of superfluid hydrodynamics, in which quantized vortices play a significant role. The recent research on superfluid turbulence enters a new stage rather different from the old ones chiefly devoted to thermal counterflow. After describing the current motivation on these topics, we discuss our research which studies the energy spectrum both by the vortex filament model and the Gross-Pitaevskii model. Both energy spectra are consistent with the Kolmogorov law, which shows a close similarity between superfluid (quantum) and classical turbulence.

Kluwer Academic Publishers eBooks•May 4, 2006•0 citations

Inertial Range and the Kolmogorov Spectrum of Quantum Turbulence

Makoto Tsubota, Michikazu Kobayashi

Quantum turbulence is numerically studied by solving the Gross‐Pitaevskii equation. By introducing both energy dissipation at small scales and energy injection at large scales, we succeed in obtaining steady turbulence sustained by a balance between energy injection and energy dissipation. The energy spectrum in the inertial range takes the form of the Kolmogorov spectrum and the energy flux is consistent with the energy dissipation rate at small scales. These results reveal the properties of quantum turbulence in the inertial range, allowing us to propose a prototype of turbulence much simpler than conventional classical turbulence.

arXiv:cond-mat/0507049•AIP conference proceedings•Jan 1, 2006•1 citation

Theoretical Analysis of the Energy Cascade in Quantum Turbulence: From Richardson–Kolmogorov Eddies to Kelvin Waves

Abishek Mahalingam

Abstract Quantum turbulence — the chaotic, non-equilibrium state of a superfluid threaded by a dense tangle of quantized vortex lines — provides a uniquely clean testbed for the universal statistical mechanics of turbulent energy transfer. We develop a theoretical account of the energy cascade across all relevant length scales: from macroscopic, quasi-classical Richardson–Kolmogorov eddies, through the dimensionally frustrated L’vov–Nazarenko–Rudenko (LNR) bottleneck at the mean inter-vortex spacing, down to the weakly nonlinear Kelvin-wave cascade on individual filaments, and finally to the zero-temperature dissipation cutoff. Starting from the Gross–Pitaevskii equation and its Madelung hydrodynamic decomposition, we separate the compressible and incompressible components of the flow to isolate the vortical and acoustic energy channels. Vortex reconnection is identified as the microscopic mechanism coupling these regimes, and the competing predictions of the Vortex Filament Model and the Gross–Pitaevskii equation for reconnection dynamics are compared. We review the theoretical controversy between the Kozik–Svistunov six-wave cascade and the L’vov–Nazarenko four-wave cascade, together with the associated tilt-symmetry debate, and present the finite-temperature two-fluid (HVBK) description, showing how mutual friction locks the normal and superfluid components at large scales while damping Kelvin waves at small scales. PACS numbers: 67.25.dk, 47.37.+q, 03.75.Kk, 47.32.C−

•Jul 10, 2026•0 citations
We investigated dynamics of superfluid turbulence by the Gross-Pitaevskii equation and its relation to conventional classical turbulence. We introduced the dissipation term which is effective only in the scale smaller than the core size of quantized vortices, and found that the energy spectrum of superfluid turbulence was consistent with the Kolmogorov law which is one of the most important statistical laws of classical turbulence.
There is a growing interest in the relation between classical turbulence and quantum turbulence. Classical turbulence arises from complicated dynamics of eddies in a classical fluid. In contrast, quantum turbulence consists of a tangle of stable topological defects called quantized vortices, and thus quantum turbulence provides a simpler prototype of turbulence than classical turbulence. In this paper, we investigate the dynamics and statistics of quantized vortices in quantum turbulence by numerically solving a modified Gross-Pitaevskii equation. First, to make decaying turbulence, we introduce a dissipation term that works only at scales below the healing length. Second, to obtain steady turbulence through the balance between injection and decay, we add energy injection at large scales. The energy spectrum is quantitatively consistent with the Kolmogorov law in both decaying and steady turbulence. Consequently, this is the first study that confirms the inertial range of quantum turbulence.
Large scale numerical simulation of quantum turbulence is performed by using 3-D time-dependent Gross-Pitaevskii equation.The energy spectrum obeying Kolmogorov law and large scale self-similar structure of quantum vortex tangle are found in a fully developed dumped turbulent state.Width of the inertial range becomes large depending on the system size of the simulation that is consistent with the result of the normal fluid turbulence.On the other hand, bottleneck effect near coherent length prevents the inertial range from extending to smaller scale.
Superfluid turbulence has been one of the most important problems of superfluid hydrodynamics, in which quantized vortices play a significant role. The recent research on superfluid turbulence enters a new stage rather different from the old ones chiefly devoted to thermal counterflow. After describing the current motivation on these topics, we discuss our research which studies the energy spectrum both by the vortex filament model and the Gross-Pitaevskii model. Both energy spectra are consistent with the Kolmogorov law, which shows a close similarity between superfluid (quantum) and classical turbulence.
Quantum turbulence is numerically studied by solving the Gross‐Pitaevskii equation. By introducing both energy dissipation at small scales and energy injection at large scales, we succeed in obtaining steady turbulence sustained by a balance between energy injection and energy dissipation. The energy spectrum in the inertial range takes the form of the Kolmogorov spectrum and the energy flux is consistent with the energy dissipation rate at small scales. These results reveal the properties of quantum turbulence in the inertial range, allowing us to propose a prototype of turbulence much simpler than conventional classical turbulence.
Abstract Quantum turbulence — the chaotic, non-equilibrium state of a superfluid threaded by a dense tangle of quantized vortex lines — provides a uniquely clean testbed for the universal statistical mechanics of turbulent energy transfer. We develop a theoretical account of the energy cascade across all relevant length scales: from macroscopic, quasi-classical Richardson–Kolmogorov eddies, through the dimensionally frustrated L’vov–Nazarenko–Rudenko (LNR) bottleneck at the mean inter-vortex spacing, down to the weakly nonlinear Kelvin-wave cascade on individual filaments, and finally to the zero-temperature dissipation cutoff. Starting from the Gross–Pitaevskii equation and its Madelung hydrodynamic decomposition, we separate the compressible and incompressible components of the flow to isolate the vortical and acoustic energy channels. Vortex reconnection is identified as the microscopic mechanism coupling these regimes, and the competing predictions of the Vortex Filament Model and the Gross–Pitaevskii equation for reconnection dynamics are compared. We review the theoretical controversy between the Kozik–Svistunov six-wave cascade and the L’vov–Nazarenko four-wave cascade, together with the associated tilt-symmetry debate, and present the finite-temperature two-fluid (HVBK) description, showing how mutual friction locks the normal and superfluid components at large scales while damping Kelvin waves at small scales. PACS numbers: 67.25.dk, 47.37.+q, 03.75.Kk, 47.32.C−