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Verma AK, Shukla S, Shukla V, Basu A, Pandit R. Statistical properties of superfluid turbulence in ^{4}He from the Hall-Vinen-Bekharevich-Khalatnikov model. Phys Rev E 2023; 108:045103. [PMID: 37978641 DOI: 10.1103/physreve.108.045103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2023] [Accepted: 09/08/2023] [Indexed: 11/19/2023]
Abstract
We obtain the von Kármán-Howarth relation for the stochastically forced three-dimensional (3D) Hall-Vinen-Bekharevich-Khalatnikov (HVBK) model of superfluid turbulence in helium (^{4}He) by using the generating-functional approach. We combine direct numerical simulations (DNSs) and analytical studies to show that, in the statistically steady state of homogeneous and isotropic superfluid turbulence, in the 3D HVBK model, the probability distribution function (PDF) P(γ), of the ratio γ of the magnitude of the normal fluid velocity and superfluid velocity, has power-law tails that scale as P(γ)∼γ^{3}, for γ≪1, and P(γ)∼γ^{-3}, for γ≫1. Furthermore, we show that the PDF P(θ) of the angle θ between the normal-fluid velocity and superfluid velocity exhibits the following power-law behaviors: P(θ)∼θ for θ≪θ_{*} and P(θ)∼θ^{-4} for θ_{*}≪θ≪1, where θ_{*} is a crossover angle that we estimate. From our DNSs we obtain energy, energy-flux, and mutual-friction-transfer spectra, as well as the longitudinal-structure-function exponents for the normal fluid and the superfluid, as a function of the temperature T, by using the experimentally determined mutual-friction coefficients for superfluid helium ^{4}He, so our results are of direct relevance to superfluid turbulence in this system.
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Affiliation(s)
- Akhilesh Kumar Verma
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - Sanjay Shukla
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - Vishwanath Shukla
- Department of Physics, Indian Institute of Technology, Kharagpur, Kharagpur 721302, India
| | - Abhik Basu
- Theory Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Calcutta 700064, West Bengal, India
| | - Rahul Pandit
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
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Turbulence in a matter-wave supersolid. Sci Rep 2018; 8:12589. [PMID: 30135502 PMCID: PMC6105649 DOI: 10.1038/s41598-018-30852-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2018] [Accepted: 08/01/2018] [Indexed: 11/08/2022] Open
Abstract
Quantum turbulence associated with wave and vortex dynamics is numerically investigated for a two-dimensional trapped atomic Rydberg-dressed Bose-Einstein condensate (BEC). When the coupling constant of the soft-core interaction is over a critical value, the superfluid (SF) system can transition into a hexagonal supersolid (SS) state. Based on the Gross-Pitaevskii equation approach, we have discovered a new characteristic k-13/3 scaling law for wave turbulence in the SS state, that coexists with the waveaction k-1/3 and energy k-1 cascades commonly existing in a SF BEC. The new k-13/3 scaling law implies that the SS system exhibits a negative, minus-one power energy dispersion (E ~ k-1) at the wavevector consistent with the radius of the SS droplet. For vortex turbulence, in addition to the presence of the Kolmogorov energy k-5/3 and Saffman enstrophy k-4 cascades, it is found that large amount of independent vortices and antivortices pinned to the interior of the oscillating SS results in a strong k-1 scaling at the wavevector consistent with the SS lattice constant.
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Lin PC, I L. Interacting Multiscale Acoustic Vortices as Coherent Excitations in Dust Acoustic Wave Turbulence. PHYSICAL REVIEW LETTERS 2018; 120:135004. [PMID: 29694209 DOI: 10.1103/physrevlett.120.135004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2017] [Revised: 02/02/2018] [Indexed: 06/08/2023]
Abstract
In this work, using three-dimensional intermittent dust acoustic wave turbulence in a dusty plasma as a platform and multidimensional empirical mode decomposition into different-scale modes in the 2+1D spatiotemporal space, we demonstrate the experimental observation of the interacting multiscale acoustic vortices, winding around wormlike amplitude hole filaments coinciding with defect filaments, as the basic coherent excitations for acoustic-type wave turbulence. For different decomposed modes, the self-similar rescaled stretched exponential lifetime histograms of amplitude hole filaments, and the self-similar power spectra of dust density fluctuations, indicate that similar dynamical rules are followed over a wide range of scales. In addition to the intermode acoustic vortex pair generation, propagation, or annihilation, the intra- and intermode interactions of acoustic vortices with the same or opposite helicity, their entanglement and synchronization, are found to be the key dynamical processes in acoustic wave turbulence, akin to the interacting multiscale vortices around wormlike cores observed in hydrodynamic turbulence.
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Affiliation(s)
- Po-Cheng Lin
- Department of Physics and Center for Complex Systems, National Central University, Jhongli 320, Taiwan, Republic of China
| | - Lin I
- Department of Physics and Center for Complex Systems, National Central University, Jhongli 320, Taiwan, Republic of China
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Emergence of a turbulent cascade in a quantum gas. Nature 2016; 539:72-75. [DOI: 10.1038/nature20114] [Citation(s) in RCA: 124] [Impact Index Per Article: 15.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2016] [Accepted: 09/10/2016] [Indexed: 11/08/2022]
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Shukla V, Pandit R. Multiscaling in superfluid turbulence: A shell-model study. Phys Rev E 2016; 94:043101. [PMID: 27841527 DOI: 10.1103/physreve.94.043101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2015] [Indexed: 06/06/2023]
Abstract
We examine the multiscaling behavior of the normal- and superfluid-velocity structure functions in three-dimensional superfluid turbulence by using a shell model for the three-dimensional (3D) Hall-Vinen-Bekharevich-Khalatnikov (HVBK) equations. Our 3D-HVBK shell model is based on the Gledzer-Okhitani-Yamada shell model. We examine the dependence of the multiscaling exponents on the normal-fluid fraction and the mutual-friction coefficients. Our extensive study of the 3D-HVBK shell model shows that the multiscaling behavior of the velocity structure functions in superfluid turbulence is more complicated than it is in fluid turbulence.
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Affiliation(s)
- Vishwanath Shukla
- Laboratoire de Physique Statistique de l'Ecole Normale Supérieure, 24 Rue Lhomond, 75231 Paris, France
| | - Rahul Pandit
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
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Rosenberg D, Marino R, Herbert C, Pouquet A. Variations of characteristic time scales in rotating stratified turbulence using a large parametric numerical study. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2016; 39:8. [PMID: 26830757 DOI: 10.1140/epje/i2016-16008-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2015] [Accepted: 01/04/2016] [Indexed: 06/05/2023]
Abstract
We study rotating stratified turbulence (RST) making use of numerical data stemming from a large parametric study varying the Reynolds, Froude and Rossby numbers, Re, Fr and Ro in a broad range of values. The computations are performed using periodic boundary conditions on grids of 1024(3) points, with no modeling of the small scales, no forcing and with large-scale random initial conditions for the velocity field only, and there are altogether 65 runs analyzed in this paper. The buoyancy Reynolds number defined as R(B) = ReFr2 varies from negligible values to ≈ 10(5), approaching atmospheric or oceanic regimes. This preliminary analysis deals with the variation of characteristic time scales of RST with dimensionless parameters, focusing on the role played by the partition of energy between the kinetic and potential modes, as a key ingredient for modeling the dynamics of such flows. We find that neither rotation nor the ratio of the Brunt-Väisälä frequency to the inertial frequency seem to play a major role in the absence of forcing in the global dynamics of the small-scale kinetic and potential modes. Specifically, in these computations, mostly in regimes of wave turbulence, characteristic times based on the ratio of energy to dissipation of the velocity and temperature fluctuations, T(V) and T(P), vary substantially with parameters. Their ratio γ=T(V)/T(P) follows roughly a bell-shaped curve in terms of Richardson number Ri. It reaches a plateau - on which time scales become comparable, γ≈0.6 - when the turbulence has significantly strengthened, leading to numerous destabilization events together with a tendency towards an isotropization of the flow.
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Affiliation(s)
- D Rosenberg
- Oak Ridge National Laboratory, National Center for Computational Sciences, P.O. Box 2008, 37831, Oak Ridge, TN, USA
- SciTec, Inc., 100 Wall St., 08540, Princeton, NJ, USA
| | - R Marino
- École Normale Supérieure, F-69007, Lyon, France
- Space Sciences Laboratory, University of California, 94720, Berkeley, CA, USA
| | - C Herbert
- Department of Physics of Complex Systems, Weizmann Institute of Science, 76100, Rehovot, Israel
| | - A Pouquet
- Laboratory for Atmospheric and Space Physics, University of Colorado, 80309, Boulder, CO, USA.
- National Center for Atmospheric Research, P.O. Box 3000, 80307, Boulder, CO, USA.
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Berman OL, Kezerashvili RY, Kolmakov GV, Pomirchi LM. Spontaneous formation and nonequilibrium dynamics of a soliton-shaped Bose-Einstein condensate in a trap. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:062901. [PMID: 26172766 DOI: 10.1103/physreve.91.062901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2015] [Indexed: 06/04/2023]
Abstract
The Bose-stimulated self-organization of a quasi-two-dimensional nonequilibrium Bose-Einstein condensate in an in-plane potential is proposed. We obtained the solution of the nonlinear, driven-dissipative Gross-Pitaevskii equation for a Bose-Einstein condensate trapped in an external asymmetric parabolic potential within the method of the spectral expansion. We found that, in sharp contrast to previous observations, the condensate can spontaneously acquire a solitonlike shape for spatially homogeneous pumping. This condensate soliton performs oscillatory motion in a parabolic trap and, also, can spontaneously rotate. Stability of the condensate soliton in the spatially asymmetric trap is analyzed. In addition to the nonlinear dynamics of nonequilibrium Bose-Einstein condensates of ultracold atoms, our findings can be applied to the condensates of quantum well excitons and cavity polaritons in semiconductor heterostructure, and to the condensates of photons.
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Affiliation(s)
- Oleg L Berman
- Physics Department, New York City College of Technology, The City University of New York, Brooklyn, New York 11201, USA
| | - Roman Ya Kezerashvili
- Physics Department, New York City College of Technology, The City University of New York, Brooklyn, New York 11201, USA
| | - German V Kolmakov
- Physics Department, New York City College of Technology, The City University of New York, Brooklyn, New York 11201, USA
| | - Leonid M Pomirchi
- Physics Department, New York City College of Technology, The City University of New York, Brooklyn, New York 11201, USA
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Barenghi CF, Skrbek L, Sreenivasan KR. Introduction to quantum turbulence. Proc Natl Acad Sci U S A 2014; 111 Suppl 1:4647-52. [PMID: 24704870 PMCID: PMC3970860 DOI: 10.1073/pnas.1400033111] [Citation(s) in RCA: 194] [Impact Index Per Article: 19.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The term quantum turbulence denotes the turbulent motion of quantum fluids, systems such as superfluid helium and atomic Bose-Einstein condensates, which are characterized by quantized vorticity, superfluidity, and, at finite temperatures, two-fluid behavior. This article introduces their basic properties, describes types and regimes of turbulence that have been observed, and highlights similarities and differences between quantum turbulence and classical turbulence in ordinary fluids. Our aim is also to link together the articles of this special issue and to provide a perspective of the future development of a subject that contains aspects of fluid mechanics, atomic physics, condensed matter, and low-temperature physics.
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Affiliation(s)
- Carlo F. Barenghi
- Joint Quantum Centre Durham-Newcastle and School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom
| | - Ladislav Skrbek
- Faculty of Mathematics and Physics, Charles University, 12116 Prague, Czech Republic; and
| | - Katepalli R. Sreenivasan
- Department of Physics and Courant Institute of Mathematical Sciences, New York University, New York, NY 10012
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