Possibility of Inverse Energy Cascade in Two-Dimensional Quantum Turbulence

Numasato, Ryu; Tsubota, Makoto

doi:10.1007/s10909-009-9965-0

Cited by 30 publications

(40 citation statements)

References 15 publications

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“…It is noticeable that the two-body decay rate, Γ 2 , shows a faster response to the temperature than the one-body decay rate, Γ 1 , and this seems to imply that the physical mechanisms determining each decay rate are different. The power-law fits to Γ 1 (T ) and Γ 2 (T ) give the exponents of 0.87(20) and 1.88 (12), respectively, showing almost linear and quadratic dependence on the temperature. Here, we assume that the decay rates vanish at T = 0.…”

Section: Temperaturementioning

confidence: 96%

“…An interesting question is whether the inverse cascade can occur in an atomic BEC. Since the enstrophy, proportional to the total number of quantized vortices in quantum turbulence, is not conserved in a compressible 2D superfluid due to the vortex-antivortex annihilation, there has been a theoretical controversy on this issue [11][12][13][14][15][16][17][18][19][20]. Recently, Neely et al [21] reported an experimental and numerical study to show that there are conditions for which 2D turbulence in a BEC can dissipatively evolve into large-scale flow.…”

Section: Introductionmentioning

confidence: 99%

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Relaxation of superfluid turbulence in highly oblate Bose-Einstein condensates

et al. 2014

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We investigate thermal relaxation of superfluid turbulence in a highly oblate Bose-Einstein condensate. We generate turbulent flow in the condensate by sweeping the center region of the condensate with a repulsive optical potential. The turbulent condensate shows a spatially disordered distribution of quantized vortices and the vortex number of the condensate exhibits nonexponential decay behavior which we attribute to the vortex pair annihilation. The vortex-antivortex collisions in the condensate are identified with crescent-shaped, coalesced vortex cores. We observe that the nonexponential decay of the vortex number is quantitatively well described by a rate equation consisting of one-body and two-body decay terms. In our measurement, we find that the local two-body decay rate is closely proportional to T 2 /µ, where T is the temperature and µ is the chemical potential.

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Section: Temperaturementioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Relaxation of superfluid turbulence in highly oblate Bose-Einstein condensates

et al. 2014

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“…Several works have considered the possibility of an inverse energy cascade in two-dimensional BECs, suggesting that the compressibility of the fluid may be fatal for largescale clustering, instead causing transport of energy to small scales driven by vortex dipole annihilation [56][57][58]. However, these works considered specific scenarios that immediately prohibited clustering, due to either starting from initial conditions dominated by acoustic energy [56,57], or evolving the system according to an overdamped equation of motion [58].…”

Section: B Motivation From Bose-einstein Condensatesmentioning

confidence: 99%

“…However, these works considered specific scenarios that immediately prohibited clustering, due to either starting from initial conditions dominated by acoustic energy [56,57], or evolving the system according to an overdamped equation of motion [58]. As shown in a systematic study of energy transport [44], a clear regime exists where energy is transported to large scales via a vortex clustering process.…”

Section: B Motivation From Bose-einstein Condensatesmentioning

confidence: 99%

Theory of the vortex-clustering transition in a confined two-dimensional quantum fluid

Billam

Nian

et al. 2016

Phys. Rev. A

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Clustering of like-sign vortices in a planar bounded domain is known to occur at negative temperature, a phenomenon that Onsager demonstrated to be a consequence of bounded phase space. In a confined superfluid, quantized vortices can support such an ordered phase, provided they evolve as an almost isolated subsystem containing sufficient energy. A detailed theoretical understanding of the statistical mechanics of such states thus requires a microcanonical approach. Here we develop an analytical theory of the vortex clustering transition in a neutral system of quantum vortices confined to a two-dimensional disk geometry, within the microcanonical ensemble. The choice of ensemble is essential for identifying the correct thermodynamic limit of the system, enabling a rigorous description of clustering in the language of critical phenomena. As the system energy increases above a critical value, the system develops global order via the emergence of a macroscopic dipole structure from the homogeneous phase of vortices, spontaneously breaking the Z 2 symmetry associated with invariance under vortex circulation exchange, and the rotational SO(2) symmetry due to the disk geometry. The dipole structure emerges characterized by the continuous growth of the macroscopic dipole moment which serves as a global order parameter, resembling a continuous phase transition. The critical temperature of the transition, and the critical exponent associated with the dipole moment, are obtained exactly within mean-field theory. The clustering transition is shown to be distinct from the final state reached at high energy, known as supercondensation. The dipole moment develops via two macroscopic vortex clusters and the cluster locations are found analytically, both near the clustering transition and in the supercondensation limit. The microcanonical theory shows excellent agreement with Monte Carlo simulations, and signatures of the transition are apparent even for a modest system of 100 vortices, accessible in current Bose-Einstein condensate experiments.

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“…In superfluids, the enstrophy Ω coincides (up to a prefactor) with the total number of quantized vortex points [25]. In GP dynamics the total number of vortices is not conserved.…”

Section: Introductionmentioning

confidence: 99%

Direct energy cascade in two-dimensional compressible quantum turbulence

2010

Self Cite

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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) ∝ k −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.

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Possibility of Inverse Energy Cascade in Two-Dimensional Quantum Turbulence

Cited by 30 publications

References 15 publications

Relaxation of superfluid turbulence in highly oblate Bose-Einstein condensates

Relaxation of superfluid turbulence in highly oblate Bose-Einstein condensates

Theory of the vortex-clustering transition in a confined two-dimensional quantum fluid

Direct energy cascade in two-dimensional compressible quantum turbulence

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