arXiv:cond-mat/0507049 · AIP conference proceedings

Inertial Range and the Kolmogorov Spectrum of Quantum Turbulence

Makoto Tsubota, Michikazu Kobayashi

Published Jan 1, 2006• 1 citation

Abstract

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.

DOI: 10.1063/1.2354673

Related papers

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/0508624Journal of the Physical Society of JapanDec 1, 200595 citations

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/0411750Physical Review LettersFeb 14, 2005223 citations

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

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.

物性研究Jun 20, 20050 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 TechnologyOct 1, 20112 citations

Direct energy cascade in two-dimensional compressible quantum turbulence

Ryu Numasato, Makoto Tsubota, Victor S. L’vov

We numerically study two-dimensional quantum turbulence with a Gross-Pitaevskii model. With the energy initially accumulated at large scale, quantum turbulence with many quantized vortex points is generated. Due to the lack of enstrophy conservation in this model, direct energy cascade with a Kolmogorov-Obukhov energy spectrum $E(k)\ensuremath{\propto}{k}^{\ensuremath{-}5/3}$ is observed, which is quite different from two-dimensional incompressible classical turbulence in the decaying case. A positive value for the energy flux guarantees a direct energy cascade in the inertial range (from large to small scales). After almost all the energy at the large scale cascades to the small scale, the compressible kinetic energy realizes the thermodynamic equilibrium state without quantized vortices.

arXiv:1002.3667Physical Review AJun 24, 201093 citations

Unitary Qubit Lattice Gas Representation of 2D and 3D Quantum Turbulence

George Vahala, Bo Zhang, Jeffrey Yepez +2 more

Turbulence is of vital interest and importance to the study of fluid dynamics Pope (1990). In classical physics, turbulence was first studied carefully for incompressible flows whose evolution was given by the Navier-Stokes equations. One of the most celebrated results of incompressible classical turbulence (CT) is the existence of an inertial range with the cascade of kinetic energy from large to small spatial scales until one reaches scale lengths on the order of the dissipationwave length and the eddies/vortices are destroyed. The Kolmogorov kinetic energy spectrum in this inertial range follows the power law in wave number space.

InTech eBooksMar 9, 201210 citations