1
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Kolokolov IV, Lebedev VV, Parfenyev VM. Correlations in a weakly interacting two-dimensional random flow. Phys Rev E 2024; 109:035103. [PMID: 38632784 DOI: 10.1103/physreve.109.035103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2023] [Accepted: 02/15/2024] [Indexed: 04/19/2024]
Abstract
We analytically examine fluctuations of vorticity excited by an external random force in two-dimensional fluid. We develop the perturbation theory enabling one to calculate nonlinear corrections to correlation functions of the flow fluctuations found in the linear approximation. We calculate the correction to the pair correlation function and the triple correlation function. It enables us to establish the criterion of validity of the perturbation theory for different ratios of viscosity and bottom friction. We find that the corrections to the second moment are anomalously weak in the cases of small bottom friction and small viscosity and relate the weakness to the energy and enstrophy balances. We demonstrate that at small bottom friction the triple correlation function is characterized by universal scaling behavior in some region of lengths. The developed perturbation method was verified and confirmed by direct numerical simulations.
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Affiliation(s)
- I V Kolokolov
- Landau Institute for Theoretical Physics, RAS, 142432, Chernogolovka, Moscow region, Russia and National Research University Higher School of Economics, 101000, Myasnitskaya ul. 20, Moscow, Russia
| | - V V Lebedev
- Landau Institute for Theoretical Physics, RAS, 142432, Chernogolovka, Moscow region, Russia and National Research University Higher School of Economics, 101000, Myasnitskaya ul. 20, Moscow, Russia
| | - V M Parfenyev
- Landau Institute for Theoretical Physics, RAS, 142432, Chernogolovka, Moscow region, Russia and National Research University Higher School of Economics, 101000, Myasnitskaya ul. 20, Moscow, Russia
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2
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Svirsky A, Herbert C, Frishman A. Statistics of inhomogeneous turbulence in large-scale quasigeostrophic dynamics. Phys Rev E 2023; 108:065102. [PMID: 38243459 DOI: 10.1103/physreve.108.065102] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2023] [Accepted: 10/19/2023] [Indexed: 01/21/2024]
Abstract
A remarkable feature of two-dimensional turbulence is the transfer of energy from small to large scales. This process can result in the self-organization of the flow into large, coherent structures due to energy condensation at the largest scales. We investigate the formation of this condensate in a quasigeostropic flow in the limit of small Rossby deformation radius, namely the large-scale quasigeostrophic model. In this model potential energy is transferred up-scale while kinetic energy is transferred down-scale in a direct cascade. We focus on a jet mean flow and carry out a thorough investigation of the second-order statistics for this flow, combining a quasilinear analytical approach with direct numerical simulations. We show that the quasilinear approach applies in regions where jets are strong and is able to capture all second-order correlators in that region, including those related to the kinetic energy. This is a consequence of the blocking of the direct cascade by the mean flow in jet regions, suppressing fluctuation-fluctuation interactions. The suppression of the direct cascade is demonstrated using a local coarse-graining approach allowing us to measure space dependent interscale kinetic energy fluxes, which we show are concentrated in between jets in our simulations. We comment on the possibility of a similar direct cascade arrest in other two-dimensional flows, arguing that it is a special feature of flows in which the fluid element interactions are local in space.
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Affiliation(s)
- Anton Svirsky
- Physics Department, Technion Israel Institute of Technology, 32000 Haifa, Israel
| | - Corentin Herbert
- ENS de Lyon, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - Anna Frishman
- Physics Department, Technion Israel Institute of Technology, 32000 Haifa, Israel
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3
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Svirsky A, Herbert C, Frishman A. Two-Dimensional Turbulence with Local Interactions: Statistics of the Condensate. PHYSICAL REVIEW LETTERS 2023; 131:224003. [PMID: 38101360 DOI: 10.1103/physrevlett.131.224003] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2023] [Revised: 09/03/2023] [Accepted: 10/24/2023] [Indexed: 12/17/2023]
Abstract
Two-dimensional turbulence self-organizes through a process of energy accumulation at large scales, forming a coherent flow termed a condensate. We study the condensate in a model with local dynamics, the large-scale quasigeostrophic equation, observed here for the first time. We obtain analytical results for the mean flow and the two-point, second-order correlation functions, and validate them numerically. The condensate state requires partiy+time-reversal symmetry breaking. We demonstrate distinct universal mechanisms for the even and odd correlators under this symmetry. We find that the model locality is imprinted in the small scale dynamics, which the condensate spatially confines.
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Affiliation(s)
- Anton Svirsky
- Physics Department, Technion Israel Institute of Technology, 32000 Haifa, Israel
| | - Corentin Herbert
- ENS de Lyon, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - Anna Frishman
- Physics Department, Technion Israel Institute of Technology, 32000 Haifa, Israel
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4
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Whittaker T, Janik RA, Oz Y. Neural network complexity of chaos and turbulence. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2023; 46:57. [PMID: 37470886 DOI: 10.1140/epje/s10189-023-00321-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2023] [Accepted: 07/10/2023] [Indexed: 07/21/2023]
Abstract
Chaos and turbulence are complex physical phenomena, yet a precise definition of the complexity measure that quantifies them is still lacking. In this work, we consider the relative complexity of chaos and turbulence from the perspective of deep neural networks. We analyze a set of classification problems, where the network has to distinguish images of fluid profiles in the turbulent regime from other classes of images such as fluid profiles in the chaotic regime, various constructions of noise and real-world images. We analyze incompressible as well as weakly compressible fluid flows. We quantify the complexity of the computation performed by the network via the intrinsic dimensionality of the internal feature representations and calculate the effective number of independent features which the network uses in order to distinguish between classes. In addition to providing a numerical estimate of the complexity of the computation, the measure also characterizes the neural network processing at intermediate and final stages. We construct adversarial examples and use them to identify the two point correlation spectra for the chaotic and turbulent vorticity as the feature used by the network for classification.
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Affiliation(s)
- Tim Whittaker
- Département des sciences de la Terre et de l'atmosphère, Université du Québec à Montréal, Montréal, QC, H3C 3P8, Canada.
| | - Romuald A Janik
- Institute of Theoretical Physics and Mark Kac Center for Complex Systems Research, Jagiellonian University, ul. Łojasiewicza 11, 30-348, Kraków, Poland
| | - Yaron Oz
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, 69978, Tel-Aviv, Israel
- Simons Center for Geometry and Physics, SUNY, Stony Brook, NY, 11794, USA
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5
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Korotkevich AO. Inverse Cascade Spectrum of Gravity Waves in the Presence of a Condensate: A Direct Numerical Simulation. PHYSICAL REVIEW LETTERS 2023; 130:264002. [PMID: 37450799 DOI: 10.1103/physrevlett.130.264002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Accepted: 05/30/2023] [Indexed: 07/18/2023]
Abstract
During the set of direct numerical simulations of the forced isotropic turbulence of surface gravity waves in the framework of primordial dynamical equations, the universal inverse cascade spectrum was observed. The slope of the spectrum is the same (in the margin of error) for different levels of pumping and nonlinearity as well as dissipation present in the system. In all simulation runs formation of the inverse cascade spectrum was accompanied by the appearance of a strong long wave background (condensate). The observed slope of the spectrum ∼k^{-3.07} is different from the constant wave action flux solution predicted by the wave turbulence theory ∼k^{-23/6}.
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Affiliation(s)
- Alexander O Korotkevich
- Department of Mathematics and Statistics, University of New Mexico, MSC01 1115, 1 University of New Mexico, Albuquerque, New Mexico 87131-0001, USA and L.D. Landau Institute for Theoretical Physics RAS, Prospekt Akademika Semenova 1A, Chernogolovka, Moscow region, 142432, Russian Federation
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6
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Rorai C, Toschi F, Pagonabarraga I. Coexistence of Active and Hydrodynamic Turbulence in Two-Dimensional Active Nematics. PHYSICAL REVIEW LETTERS 2022; 129:218001. [PMID: 36461968 DOI: 10.1103/physrevlett.129.218001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2022] [Revised: 09/29/2022] [Accepted: 10/25/2022] [Indexed: 06/17/2023]
Abstract
In active nematic liquid crystals, activity is able to drive chaotic spatiotemporal flows referred to as active turbulence. Active turbulence has been characterized through theoretical and experimental work as a low Reynolds number phenomenon. We show that, in two dimensions, the active forcing alone is able to trigger hydrodynamic turbulence leading to the coexistence of active and inertial turbulence. This type of flow develops for sufficiently active and extensile flow-aligning nematics. We observe that the combined effect of an extensile nematic and large values of the flow-aligning parameter leads to a broadening of the elastic energy spectrum that promotes a growth of kinetic energy able to trigger an inverse energy cascade.
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Affiliation(s)
- C Rorai
- CECAM, Centre Européen de Calcul Atomique et Moléculaire, École Polytechnique Fédérale de Lausanne (EPFL), Batochime, Avenue Forel 2, 1015 Lausanne, Switzerland
| | - F Toschi
- Department of Applied Physics, Eindhoven University of Technology, Den Dolech 2, 5600 MB Eindhoven, Netherlands
- CNR-IAC, I-00185 Rome, Italy
| | - I Pagonabarraga
- CECAM, Centre Européen de Calcul Atomique et Moléculaire, École Polytechnique Fédérale de Lausanne (EPFL), Batochime, Avenue Forel 2, 1015 Lausanne, Switzerland
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, C. Martí i Franquès 1, 08028 Barcelona, Spain
- University of Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, 08028 Barcelona, Spain
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7
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Parfenyev V. Profile of a two-dimensional vortex condensate beyond the universal limit. Phys Rev E 2022; 106:025102. [PMID: 36109998 DOI: 10.1103/physreve.106.025102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2022] [Accepted: 07/25/2022] [Indexed: 06/15/2023]
Abstract
It is well known that an inverse turbulent cascade in a finite (2π×2π) two-dimensional periodic domain leads to the emergence of a system-sized coherent vortex dipole. We report a numerical hyperviscous study of the spatial vorticity profile inside one of the vortices. The exciting force was shortly correlated in time, random in space, and had a correlation length l_{f}=2π/k_{f} with k_{f} ranging from 100 to 12.5. Previously, it was found that in the asymptotic limit of small-scale forcing, the vorticity exhibits the power-law behavior Ω(r)=(3ε/α)^{1/2}r^{-1}, where r is the distance to the vortex center, α is the bottom friction coefficient, and ε is the inverse energy flux. Now we show that for a spatially homogeneous forcing with finite k_{f} the vorticity profile becomes steeper, with the difference increasing with the pumping scale but decreasing with the Reynolds number at the forcing scale. Qualitatively, this behavior is related to a decrease in the effective pumping of the coherent vortex with distance from its center. To support this statement, we perform an additional simulation with spatially localized forcing, in which the effective pumping of the coherent vortex, on the contrary, increases with r, and show that in this case the vorticity profile can be flatter than the asymptotic limit.
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Affiliation(s)
- Vladimir Parfenyev
- Landau Institute for Theoretical Physics, Russian Academy of Sciences, 1-A Akademika Semenova av., 142432 Chernogolovka, Russia and National Research University Higher School of Economics, Faculty of Physics, Myasnitskaya 20, 101000 Moscow, Russia
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8
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Rigon G, Albertazzi B, Pikuz T, Mabey P, Bouffetier V, Ozaki N, Vinci T, Barbato F, Falize E, Inubushi Y, Kamimura N, Katagiri K, Makarov S, Manuel MJE, Miyanishi K, Pikuz S, Poujade O, Sueda K, Togashi T, Umeda Y, Yabashi M, Yabuuchi T, Gregori G, Kodama R, Casner A, Koenig M. Micron-scale phenomena observed in a turbulent laser-produced plasma. Nat Commun 2021; 12:2679. [PMID: 33976145 PMCID: PMC8113596 DOI: 10.1038/s41467-021-22891-w] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2020] [Accepted: 03/29/2021] [Indexed: 11/09/2022] Open
Abstract
Turbulence is ubiquitous in the universe and in fluid dynamics. It influences a wide range of high energy density systems, from inertial confinement fusion to astrophysical-object evolution. Understanding this phenomenon is crucial, however, due to limitations in experimental and numerical methods in plasma systems, a complete description of the turbulent spectrum is still lacking. Here, we present the measurement of a turbulent spectrum down to micron scale in a laser-plasma experiment. We use an experimental platform, which couples a high power optical laser, an x-ray free-electron laser and a lithium fluoride crystal, to study the dynamics of a plasma flow with micrometric resolution (~1μm) over a large field of view (>1 mm2). After the evolution of a Rayleigh–Taylor unstable system, we obtain spectra, which are overall consistent with existing turbulent theory, but present unexpected features. This work paves the way towards a better understanding of numerous systems, as it allows the direct comparison of experimental results, theory and numerical simulations. Turbulence effects explored use macroscale systems in general. Here the authors generate a turbulent plasma using laser irradiation of a solid target and study the dynamics of the plasma flow at the micron-scale by using scattering of an XFEL beam.
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Affiliation(s)
- G Rigon
- LULI, CNRS, CEA, École Polytechnique, UPMC, Univ Paris 06: Sorbonne Universités, Institut Polytechnique de Paris, F-91128 Palaiseau cedex, France.
| | - B Albertazzi
- LULI, CNRS, CEA, École Polytechnique, UPMC, Univ Paris 06: Sorbonne Universités, Institut Polytechnique de Paris, F-91128 Palaiseau cedex, France
| | - T Pikuz
- Institute for Open and Transdisciplinary Research Initiative, Osaka University, Osaka, Japan.,Joint Institute for High Temperatures RAS, Moscow, Russia
| | - P Mabey
- LULI, CNRS, CEA, École Polytechnique, UPMC, Univ Paris 06: Sorbonne Universités, Institut Polytechnique de Paris, F-91128 Palaiseau cedex, France
| | - V Bouffetier
- Université de Bordeaux-CNRS-CEA, CELIA, UMR 5107, Talence, France
| | - N Ozaki
- Graduate School of Engineering, Osaka University, Osaka, Japan.,Institute of Laser Engineering, Osaka University, Suita, Osaka, Japan
| | - T Vinci
- LULI, CNRS, CEA, École Polytechnique, UPMC, Univ Paris 06: Sorbonne Universités, Institut Polytechnique de Paris, F-91128 Palaiseau cedex, France
| | - F Barbato
- Université de Bordeaux-CNRS-CEA, CELIA, UMR 5107, Talence, France
| | | | - Y Inubushi
- Japan Synchrotron Radiation Research Institute, Hyogo, Japan.,RIKEN SPring-8 Center, Hyogo, Japan
| | - N Kamimura
- Graduate School of Engineering, Osaka University, Osaka, Japan
| | - K Katagiri
- Graduate School of Engineering, Osaka University, Osaka, Japan
| | - S Makarov
- Joint Institute for High Temperatures RAS, Moscow, Russia.,Department of Physics of accelerators and radiation medicine, Faculty of Physics, Lomonosov Moscow State University, Moscow, Russia
| | - M J-E Manuel
- General Atomics, Inertial Fusion Technologies, San Diego, CA, USA
| | | | - S Pikuz
- Joint Institute for High Temperatures RAS, Moscow, Russia.,National Research Nuclear University 'MEPhi', Moscow, Russia
| | - O Poujade
- CEA-DAM, DIF, Arpajon, France.,Université Paris-Saclay, CEA, LMCE, Bruyères-le-Châtel, France
| | - K Sueda
- RIKEN SPring-8 Center, Hyogo, Japan
| | - T Togashi
- Japan Synchrotron Radiation Research Institute, Hyogo, Japan.,RIKEN SPring-8 Center, Hyogo, Japan
| | - Y Umeda
- Graduate School of Engineering, Osaka University, Osaka, Japan.,Institute for Planetary Materials, Okayama University, Tottori, Japan
| | - M Yabashi
- Japan Synchrotron Radiation Research Institute, Hyogo, Japan.,RIKEN SPring-8 Center, Hyogo, Japan
| | - T Yabuuchi
- Japan Synchrotron Radiation Research Institute, Hyogo, Japan.,RIKEN SPring-8 Center, Hyogo, Japan
| | - G Gregori
- Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
| | - R Kodama
- Graduate School of Engineering, Osaka University, Osaka, Japan
| | - A Casner
- Université de Bordeaux-CNRS-CEA, CELIA, UMR 5107, Talence, France.,CEA-CESTA, 15 avenue des Sablières, CS 60001, 33116 Le Barp Cedex, France
| | - M Koenig
- LULI, CNRS, CEA, École Polytechnique, UPMC, Univ Paris 06: Sorbonne Universités, Institut Polytechnique de Paris, F-91128 Palaiseau cedex, France.,Graduate School of Engineering, Osaka University, Osaka, Japan
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9
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Aguirre Guzmán AJ, Madonia M, Cheng JS, Ostilla-Mónico R, Clercx HJH, Kunnen RPJ. Competition between Ekman Plumes and Vortex Condensates in Rapidly Rotating Thermal Convection. PHYSICAL REVIEW LETTERS 2020; 125:214501. [PMID: 33274985 DOI: 10.1103/physrevlett.125.214501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2020] [Revised: 07/15/2020] [Accepted: 10/23/2020] [Indexed: 06/12/2023]
Abstract
We perform direct numerical simulations of rotating Rayleigh-Bénard convection (RRBC) of fluids with low (Pr=0.1) and high (Pr≈5) Prandtl numbers in a horizontally periodic layer with no-slip bottom and top boundaries. No-slip boundaries are known to actively promote the formation of plumelike vertical disturbances, through so-called Ekman pumping, that control the ambient flow at sufficiently high rotation rates. At both Prandtl numbers, we demonstrate the presence of competing large-scale vortices (LSVs) in the bulk. Strong buoyant forcing and rotation foster the quasi-two-dimensional turbulent state of the flow that leads to the upscale transfer of kinetic energy that forms the domain-filling LSV condensate. The Ekman plumes from the boundary layers are sheared apart by the large-scale flow, yet we find that their energy feeds the upscale transfer. Our results of RRBC simulations substantiate the emergence of large-scale flows in nature regardless of the specific details of the boundary conditions.
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Affiliation(s)
- Andrés J Aguirre Guzmán
- Fluids and Flows group, Department of Applied Physics and J. M. Burgers Centre for Fluid Dynamics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands
| | - Matteo Madonia
- Fluids and Flows group, Department of Applied Physics and J. M. Burgers Centre for Fluid Dynamics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands
| | - Jonathan S Cheng
- Fluids and Flows group, Department of Applied Physics and J. M. Burgers Centre for Fluid Dynamics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands
| | | | - Herman J H Clercx
- Fluids and Flows group, Department of Applied Physics and J. M. Burgers Centre for Fluid Dynamics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands
| | - Rudie P J Kunnen
- Fluids and Flows group, Department of Applied Physics and J. M. Burgers Centre for Fluid Dynamics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands
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10
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Puggioni L, Kritsuk AG, Musacchio S, Boffetta G. Conformal invariance of weakly compressible two-dimensional turbulence. Phys Rev E 2020; 102:023107. [PMID: 32942444 DOI: 10.1103/physreve.102.023107] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2020] [Accepted: 07/22/2020] [Indexed: 11/07/2022]
Abstract
We study conformal invariance of vorticity clusters in weakly compressible two-dimensional turbulence at low Mach numbers. On the basis of very high resolution direct numerical simulation we demonstrate the scaling invariance of the inverse cascade with scaling close to Kolmogorov prediction. In this range of scales, the statistics of zero-vorticity isolines are found to be compatible with those of critical percolation, thus generalizing the results obtained in incompressible Navier-Stokes turbulence.
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Affiliation(s)
- Leonardo Puggioni
- Dipartimento di Fisica and INFN, Università di Torino, via P. Giuria 1, 10125 Torino, Italy
| | - Alexei G Kritsuk
- Center for Astrophysics and Space Sciences, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093-0424, USA
| | - Stefano Musacchio
- Dipartimento di Fisica and INFN, Università di Torino, via P. Giuria 1, 10125 Torino, Italy
| | - Guido Boffetta
- Dipartimento di Fisica and INFN, Università di Torino, via P. Giuria 1, 10125 Torino, Italy
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11
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Kolokolov IV, Lebedev VV. Coherent vortex in two-dimensional turbulence: Interplay of viscosity and bottom friction. Phys Rev E 2020; 102:023108. [PMID: 32942442 DOI: 10.1103/physreve.102.023108] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2020] [Accepted: 07/21/2020] [Indexed: 11/06/2022]
Abstract
We examine coherent vortices appearing as a result of the inverse cascade of two-dimensional turbulence in a finite box in the case of pumping with arbitrary correlation time in the quasilinear regime. We demonstrate that the existence of the vortices depends on the ratio between the values of the bottom friction coefficient α and the viscous damping of the flow fluctuations at the pumping scale νk_{f}^{2} (ν is the kinematic viscosity coefficient and k_{f} is the characteristic wave vector at the pumping scale). The coherent vortices appear if νk_{f}^{2}≫α and cannot exist if νk_{f}^{2}≪α. Therefore there is a border value α∼νk_{f}^{2} separating the regions. In numerical simulations, νk_{f}^{2}/α can be arbitrary, whereas in a laboratory experiment νk_{f}^{2}/α≲1 and the coherent vortices can be observed solely near the border value of νk_{f}^{2}/α.
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Affiliation(s)
- I V Kolokolov
- Landau Institute for Theoretical Physics, RAS, 142432, Chernogolovka, Moscow District, Russia.,Institute of Solid State Physics, RAS, 142432, Chernogolovka, Moscow District, Russia
| | - V V Lebedev
- Landau Institute for Theoretical Physics, RAS, 142432, Chernogolovka, Moscow District, Russia
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12
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Kolokolov IV, Kostenko MM. Universal moments of accelerations in two-dimensional turbulence. Phys Rev E 2020; 101:033108. [PMID: 32289923 DOI: 10.1103/physreve.101.033108] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2019] [Accepted: 03/02/2020] [Indexed: 11/07/2022]
Abstract
We consider two-dimensional turbulence in the presence of a condensate. The nondiagonal correlation functions of the Lagrangian accelerations are calculated, and it is shown that they have the same universality properties as the nondiagonal correlation functions of the velocity fluctuations.
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Affiliation(s)
- Igor V Kolokolov
- L.D. Landau Institute for Theoretical Physics, Ak. Semenova 1-A, Chernogolovka 142432, Moscow region, Russia.,National Research University Higher School of Economics, Myasnitskaya 20, Moscow 101000, Russia
| | - Maria M Kostenko
- L.D. Landau Institute for Theoretical Physics, Ak. Semenova 1-A, Chernogolovka 142432, Moscow region, Russia.,Department of Physics, Saint Petersburg State University, 7/9 Universitetskaya embankment, Saint Petersburg 199034, Russia
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13
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Linkmann M, Marchetti MC, Boffetta G, Eckhardt B. Condensate formation and multiscale dynamics in two-dimensional active suspensions. Phys Rev E 2020; 101:022609. [PMID: 32168685 DOI: 10.1103/physreve.101.022609] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2019] [Accepted: 02/05/2020] [Indexed: 11/07/2022]
Abstract
The collective effects of microswimmers in active suspensions result in active turbulence, a spatiotemporally chaotic dynamics at mesoscale, which is characterized by the presence of vortices and jets at scales much larger than the characteristic size of the individual active constituents. To describe this dynamics, Navier-Stokes-based one-fluid models driven by small-scale forces have been proposed. Here, we provide a justification of such models for the case of dense suspensions in two dimensions (2D). We subsequently carry out an in-depth numerical study of the properties of one-fluid models as a function of the active driving in view of possible transition scenarios from active turbulence to large-scale pattern, referred to as condensate, formation induced by the classical inverse energy cascade in Newtonian 2D turbulence. Using a one-fluid model it was recently shown [M. Linkmann et al., Phys. Rev. Lett 122, 214503 (2019)10.1103/PhysRevLett.122.214503] that two-dimensional active suspensions support two nonequilibrium steady states, one with a condensate and one without, which are separated by a subcritical transition. Here, we report further details on this transition such as hysteresis and discuss a low-dimensional model that describes the main features of the transition through nonlocal-in-scale coupling between the small-scale driving and the condensate.
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Affiliation(s)
- Moritz Linkmann
- Fachbereich Physik, Philipps-Universität Marburg, D-35032 Marburg, Germany
| | - M Cristina Marchetti
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - Guido Boffetta
- Dipartimento di Fisica and INFN, Università di Torino, via P. Giuria 1, 10125 Torino, Italy
| | - Bruno Eckhardt
- Fachbereich Physik, Philipps-Universität Marburg, D-35032 Marburg, Germany
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14
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Linkmann M, Boffetta G, Marchetti MC, Eckhardt B. Phase Transition to Large Scale Coherent Structures in Two-Dimensional Active Matter Turbulence. PHYSICAL REVIEW LETTERS 2019; 122:214503. [PMID: 31283308 DOI: 10.1103/physrevlett.122.214503] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2018] [Indexed: 06/09/2023]
Abstract
The collective motion of microswimmers in suspensions induce patterns of vortices on scales that are much larger than the characteristic size of a microswimmer, attaining a state called bacterial turbulence. Hydrodynamic turbulence acts on even larger scales and is dominated by inertial transport of energy. Using an established modification of the Navier-Stokes equation that accounts for the small-scale forcing of hydrodynamic flow by microswimmers, we study the properties of a dense suspension of microswimmers in two dimensions, where the conservation of enstrophy can drive an inverse cascade through which energy is accumulated on the largest scales. We find that the dynamical and statistical properties of the flow show a sharp transition to the formation of vortices at the largest length scale. The results show that 2D bacterial and hydrodynamic turbulence are separated by a subcritical phase transition.
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Affiliation(s)
- Moritz Linkmann
- Fachbereich Physik, Philipps-Universität of Marburg, D-35032 Marburg, Germany
| | - Guido Boffetta
- Dipartimento di Fisica and INFN, Università di Torino, via P. Giuria 1, 10125 Torino, Italy
| | - M Cristina Marchetti
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - Bruno Eckhardt
- Fachbereich Physik, Philipps-Universität of Marburg, D-35032 Marburg, Germany
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15
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Frishman A, Herbert C. Turbulence Statistics in a Two-Dimensional Vortex Condensate. PHYSICAL REVIEW LETTERS 2018; 120:204505. [PMID: 29864335 DOI: 10.1103/physrevlett.120.204505] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2017] [Indexed: 06/08/2023]
Abstract
Disentangling the evolution of a coherent mean-flow and turbulent fluctuations, interacting through the nonlinearity of the Navier-Stokes equations, is a central issue in fluid mechanics. It affects a wide range of flows, such as planetary atmospheres, plasmas, or wall-bounded flows, and hampers turbulence models. We consider the special case of a two-dimensional flow in a periodic box, for which the mean flow, a pair of box-size vortices called "condensate," emerges from turbulence. As was recently shown, a perturbative closure describes correctly the condensate when turbulence is excited at small scales. In this context, we obtain explicit results for the statistics of turbulence, encoded in the Reynolds stress tensor. We demonstrate that the two components of the Reynolds stress, the momentum flux and the turbulent energy, are determined by different mechanisms. It was suggested previously that the momentum flux is fixed by a balance between forcing and mean-flow advection: using unprecedently long numerical simulations, we provide the first direct evidence supporting this prediction. By contrast, combining analytical computations with numerical simulations, we show that the turbulent energy is determined only by mean-flow advection and obtain for the first time a formula describing its profile in the vortex.
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Affiliation(s)
- Anna Frishman
- Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA
- Department of Physics of Complex Systems, Weizmann Institute of Science, P.O. Box 26, Rehovot 76100, Israel
| | - Corentin Herbert
- Department of Physics of Complex Systems, Weizmann Institute of Science, P.O. Box 26, Rehovot 76100, Israel
- Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, Lyon F-69342, France
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16
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Andrés N, Galtier S, Sahraoui F. Exact scaling laws for helical three-dimensional two-fluid turbulent plasmas. Phys Rev E 2016; 94:063206. [PMID: 28085374 DOI: 10.1103/physreve.94.063206] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2016] [Indexed: 06/06/2023]
Abstract
We derive exact scaling laws for a three-dimensional incompressible helical two-fluid plasma, without the assumption of isotropy. For each ideal invariant of the two-fluid model, i.e., the total energy, the electron helicity, and the proton helicity, we derive simple scaling laws in terms of two-point increment correlation functions expressed in terms of the velocity field of each species and the magnetic field. These variables are appropriate for comparison with direct numerical simulation data and with in situ measurements in the near-Earth space over a broad range of spatial scales. Finally, using the exact scaling laws and dimensional analysis we predict the magnetic energy and electron helicity spectra for different ranges of scales.
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Affiliation(s)
- N Andrés
- LPP, École Polytechnique, F-91128 Palaiseau Cedex, France
| | - S Galtier
- LPP, École Polytechnique, F-91128 Palaiseau Cedex, France
- Departement de Physique, Université Paris-Sud, Orsay, France
| | - F Sahraoui
- LPP, École Polytechnique, F-91128 Palaiseau Cedex, France
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17
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Falkovich G. Interaction between mean flow and turbulence in two dimensions. Proc Math Phys Eng Sci 2016; 472:20160287. [PMID: 27493579 DOI: 10.1098/rspa.2016.0287] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
This short note is written to call attention to an analytic approach to the interaction of developed turbulence with mean flows of simple geometry (jets and vortices). It is instructive to compare cases in two and three dimensions and see why the former are solvable and the latter are not (yet). We present the analytical solutions for two-dimensional mean flows generated by an inverse turbulent cascade on a sphere and in planar domains of different aspect ratios. These solutions are obtained in the limit of small friction when the flow is strong while turbulence can be considered weak and treated perturbatively. I then discuss when these simple solutions can be realized and when more complicated flows may appear instead. The next step of describing turbulence statistics inside a flow and directions of possible future progress are briefly discussed at the end.
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Affiliation(s)
- Gregory Falkovich
- Weizmann Institute of Science, Rehovot 76100, Israel; Institute for Information Transmission Problems, Moscow 127994, Russia
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18
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Banerjee S, Galtier S. Chiral exact relations for helicities in Hall magnetohydrodynamic turbulence. Phys Rev E 2016; 93:033120. [PMID: 27078460 DOI: 10.1103/physreve.93.033120] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2015] [Indexed: 05/20/2023]
Abstract
Besides total energy, three-dimensional incompressible Hall magnetohydrodynamics (MHD) possesses two inviscid invariants, which are the magnetic helicity and the generalized helicity. Exact relations are derived for homogeneous (nonisotropic) stationary Hall MHD turbulence (and also for its inertialess electron MHD limit) with nonzero helicities and in the asymptotic limit of large Reynolds numbers. The universal laws are written only in terms of mixed second-order structure functions, i.e., the scalar product of two different increments. It provides, therefore, a direct measurement of the dissipation rates for the corresponding invariant flux. This study shows that the generalized helicity cascade is strongly linked to the left polarized fluctuations, while the magnetic helicity cascade is linked to the right polarized fluctuations.
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Affiliation(s)
- Supratik Banerjee
- Institut fur Geophysik und Meteorologie, Universität zu Köln, Pohligstrasse 3, D-50969 Köln, Germany
| | - Sébastien Galtier
- LPP, École polytechnique, F-91128 Palaiseau Cedex, France
- Departement de Physique, Université Paris-Sud, Orsay, France
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19
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Kolokolov IV, Lebedev VV. Structure of coherent vortices generated by the inverse cascade of two-dimensional turbulence in a finite box. Phys Rev E 2016; 93:033104. [PMID: 27078444 DOI: 10.1103/physreve.93.033104] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2015] [Indexed: 06/05/2023]
Abstract
We discuss the structure and geometrical characteristics of coherent vortices appearing as a result of the inverse cascade in two-dimensional turbulence in a finite box. We demonstrate that the universal velocity profile, established by J. Laurie et al. [Phys. Rev. Lett. 113, 254503 (2014)], corresponds to the passive regime of flow fluctuations. We find the vortex core radius and the vortex size, and we argue that the amount of vortices generated in the box depends on the system parameters.
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Affiliation(s)
- I V Kolokolov
- Landau Institute for Theoretical Physics, RAS, 142432, Chernogolovka, Moscow region, Russia
| | - V V Lebedev
- Landau Institute for Theoretical Physics, RAS, 142432, Chernogolovka, Moscow region, Russia
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20
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Seshasayanan K, Alexakis A. Critical behavior in the inverse to forward energy transition in two-dimensional magnetohydrodynamic flow. Phys Rev E 2016; 93:013104. [PMID: 26871152 DOI: 10.1103/physreve.93.013104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2015] [Indexed: 06/05/2023]
Abstract
We investigate the critical transition from an inverse cascade of energy to a forward energy cascade in a two-dimensional magnetohydrodynamic flow as the ratio of magnetic to mechanical forcing amplitude is varied. It is found that the critical transition is the result of two competing processes. The first process is due to hydrodynamic interactions and cascades the energy to the large scales. The second process couples small-scale magnetic fields to large-scale flows, transferring the energy back to the small scales via a nonlocal mechanism. At marginality the two cascades are both present and cancel each other. The phase space diagram of the transition is sketched.
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Affiliation(s)
- Kannabiran Seshasayanan
- Laboratoire de Physique Statistique, École Normale Supérieure, CNRS UMR 8550, Université Paris Diderot, Université Pierre et Marie Curie, 24 rue Lhomond, 75005 Paris, France
| | - Alexandros Alexakis
- Laboratoire de Physique Statistique, École Normale Supérieure, CNRS UMR 8550, Université Paris Diderot, Université Pierre et Marie Curie, 24 rue Lhomond, 75005 Paris, France
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21
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Iyer KP, Mazzitelli I, Bonaccorso F, Pouquet A, Biferale L. Rotating turbulence under "precession-like" perturbation. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2015; 38:128. [PMID: 26637337 DOI: 10.1140/epje/i2015-15128-x] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2015] [Accepted: 11/12/2015] [Indexed: 06/05/2023]
Abstract
The effects of changing the orientation of the rotation axis on homogeneous turbulence is considered. We perform direct numerical simulations on a periodic box of 1024(3) grid points, where the orientation of the rotation axis is changed (a) at a fixed time instant (b) regularly at time intervals commensurate with the rotation time scale. The former is characterized by a dominant inverse energy cascade whereas in the latter, the inverse cascade is stymied due to the recurrent changes in the rotation axis resulting in a strong forward energy transfer and large-scale structures that resemble those of isotropic turbulence.
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Affiliation(s)
- Kartik P Iyer
- University of Rome and INFN, 00133, Tor Vergata Rome, Italy.
| | | | | | - Annick Pouquet
- Laboratory for Atmospheric and Space Physics, University of Colorado at Boulder, 80303, Boulder, CO, USA
- Institute for Mathematics Applied to Geosciences (IMAGe), CISL, NCAR, 80307-3000, Boulder, CO, USA
| | - Luca Biferale
- University of Rome and INFN, 00133, Tor Vergata Rome, Italy
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22
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Hadid LZ, Sahraoui F, Kiyani KH, Retinò A, Modolo R, Canu P, Masters A, Dougherty MK. NATURE OF THE MHD AND KINETIC SCALE TURBULENCE IN THE MAGNETOSHEATH OF SATURN:
CASSINI
OBSERVATIONS. ACTA ACUST UNITED AC 2015. [DOI: 10.1088/2041-8205/813/2/l29] [Citation(s) in RCA: 41] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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23
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Sahoo G, Biferale L. Disentangling the triadic interactions in Navier-Stokes equations. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2015; 38:114. [PMID: 26537727 DOI: 10.1140/epje/i2015-15114-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2015] [Revised: 10/13/2015] [Accepted: 10/15/2015] [Indexed: 06/05/2023]
Abstract
We study the role of helicity in the dynamics of energy transfer in a modified version of the Navier-Stokes equations with explicit breaking of the mirror symmetry. We select different set of triads participating in the dynamics on the basis of their helicity content. In particular, we remove the negative helically polarized Fourier modes at all wave numbers except for those falling on a localized shell of wave number, |k| ~ k(m). Changing k(m) to be above or below the forcing scale, k(f), we are able to assess the energy transfer of triads belonging to different interaction classes. We observe that when the negative helical modes are present only at a wave number smaller than the forced wave numbers, an inverse energy cascade develops with an accumulation of energy on a stationary helical condensate. Vice versa, when negative helical modes are present only at a wave number larger than the forced wave numbers, a transition from backward to forward energy transfer is observed in the regime when the minority modes become energetic enough.
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Affiliation(s)
- Ganapati Sahoo
- Department of Physics and INFN, University of Rome "Tor Vergata", Via della Ricerca Scientifica 1, 00133, Rome, Italy.
| | - Luca Biferale
- Department of Physics and INFN, University of Rome "Tor Vergata", Via della Ricerca Scientifica 1, 00133, Rome, Italy
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24
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Mishra PK, Herault J, Fauve S, Verma MK. Dynamics of reversals and condensates in two-dimensional Kolmogorov flows. Phys Rev E 2015; 91:053005. [PMID: 26066247 DOI: 10.1103/physreve.91.053005] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2014] [Indexed: 11/07/2022]
Abstract
We present numerical simulations of the different two-dimensional flow regimes generated by a constant spatially periodic forcing balanced by viscous dissipation and large-scale drag with a dimensionless damping rate 1/Rh. The linear response to the forcing is a 6×6 square array of counterrotating vortices, which is stable when the Reynolds number Re or Rh are small. After identifying the sequence of bifurcations that lead to a spatially and temporally chaotic regime of the flow when Re and Rh are increased, we study the transitions between the different turbulent regimes observed for large Re by varying Rh. A large-scale circulation at the box size (the condensate state) is the dominant mode in the limit of vanishing large-scale drag (Rh large). When Rh is decreased, the condensate becomes unstable and a regime with random reversals between two large-scale circulations of opposite signs is generated. It involves a bimodal probability density function of the large-scale velocity that continuously bifurcates to a Gaussian distribution when Rh is decreased further.
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Affiliation(s)
- Pankaj Kumar Mishra
- Laboratoire de Physique Statistique, Ecole Normale Superieure, 24 Rue Lhomond, Paris, France
| | - Johann Herault
- Laboratoire de Physique Statistique, Ecole Normale Superieure, 24 Rue Lhomond, Paris, France
| | - Stephan Fauve
- Laboratoire de Physique Statistique, Ecole Normale Superieure, 24 Rue Lhomond, Paris, France
| | - Mahendra K Verma
- Department of Physics, Indian Institute of Technology, Kanpur 208 016, India
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25
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Laurie J, Boffetta G, Falkovich G, Kolokolov I, Lebedev V. Universal profile of the vortex condensate in two-dimensional turbulence. PHYSICAL REVIEW LETTERS 2014; 113:254503. [PMID: 25554886 DOI: 10.1103/physrevlett.113.254503] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2014] [Indexed: 06/04/2023]
Abstract
An inverse turbulent cascade in a restricted two-dimensional periodic domain creates a condensate-a pair of coherent system-size vortices. We perform extensive numerical simulations of this system and carry out theoretical analysis based on momentum and energy exchanges between the turbulence and the vortices. We show that the vortices have a universal internal structure independent of the type of small-scale dissipation, small-scale forcing, and boundary conditions. The theory predicts not only the vortex inner region profile, but also the amplitude, which both perfectly agree with the numerical data.
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Affiliation(s)
- Jason Laurie
- Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Guido Boffetta
- Dipartmento di Fisica and INFN, Università di Torino, via P. Giuria 1, 10125 Torino, Italy
| | - Gregory Falkovich
- Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel and Institute for Information Transmission Problems, Moscow 127994, Russia
| | - Igor Kolokolov
- Landau Institute for Theoretical Physics, Kosygina 2, Moscow 119334, Russia and Moscow Institute of Physics and Technology, Dolgoprudny, Moscow 141700, Russia
| | - Vladimir Lebedev
- Landau Institute for Theoretical Physics, Kosygina 2, Moscow 119334, Russia and Moscow Institute of Physics and Technology, Dolgoprudny, Moscow 141700, Russia
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26
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Billam TP, Reeves MT, Anderson BP, Bradley AS. Onsager-Kraichnan condensation in decaying two-dimensional quantum turbulence. PHYSICAL REVIEW LETTERS 2014; 112:145301. [PMID: 24765984 DOI: 10.1103/physrevlett.112.145301] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2013] [Indexed: 06/03/2023]
Abstract
Despite the prominence of Onsager's point-vortex model as a statistical description of 2D classical turbulence, a first-principles development of the model for a realistic superfluid has remained an open problem. Here we develop a mapping of a system of quantum vortices described by the homogeneous 2D Gross-Pitaevskii equation (GPE) to the point-vortex model, enabling Monte Carlo sampling of the vortex microcanonical ensemble. We use this approach to survey the full range of vortex states in a 2D superfluid, from the vortex-dipole gas at positive temperature to negative-temperature states exhibiting both macroscopic vortex clustering and kinetic energy condensation, which we term an Onsager-Kraichnan condensate (OKC). Damped GPE simulations reveal that such OKC states can emerge dynamically, via aggregation of small-scale clusters into giant OKC clusters, as the end states of decaying 2D quantum turbulence in a compressible, finite-temperature superfluid. These statistical equilibrium states should be accessible in atomic Bose-Einstein condensate experiments.
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Affiliation(s)
- T P Billam
- Jack Dodd Centre for Quantum Technology, Department of Physics, University of Otago, Dunedin 9016, New Zealand
| | - M T Reeves
- Jack Dodd Centre for Quantum Technology, Department of Physics, University of Otago, Dunedin 9016, New Zealand
| | - B P Anderson
- College of Optical Sciences, University of Arizona, Tucson, Arizona 85721, USA
| | - A S Bradley
- Jack Dodd Centre for Quantum Technology, Department of Physics, University of Otago, Dunedin 9016, New Zealand
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27
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Rubio AM, Julien K, Knobloch E, Weiss JB. Upscale energy transfer in three-dimensional rapidly rotating turbulent convection. PHYSICAL REVIEW LETTERS 2014; 112:144501. [PMID: 24765971 DOI: 10.1103/physrevlett.112.144501] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2013] [Indexed: 06/03/2023]
Abstract
Rotating Rayleigh-Bénard convection exhibits, in the limit of rapid rotation, a turbulent state known as geostrophic turbulence. This state is present for sufficiently large Rayleigh numbers representing the thermal forcing of the system, and is characterized by a leading order balance between the Coriolis force and pressure gradient. This turbulent state is itself unstable to the generation of depth-independent or barotropic vortex structures of ever larger scale through a process known as spectral condensation. This process involves an inverse cascade mechanism with a positive feedback loop whereby large-scale barotropic vortices organize small scale convective eddies. In turn, these eddies provide a dynamically evolving energy source for the large-scale barotropic component. Kinetic energy spectra for the barotropic dynamics are consistent with a k-3 downscale enstrophy cascade and an upscale cascade that steepens to k-3 as the box-scale condensate forms. At the same time the flow maintains a baroclinic convective component with an inertial range consistent with a k-5/3 spectrum. The condensation process resembles a similar process in two dimensions but is fully three-dimensional.
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Affiliation(s)
- Antonio M Rubio
- Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309, USA
| | - Keith Julien
- Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309, USA
| | - Edgar Knobloch
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Jeffrey B Weiss
- Department of Atmospheric and Oceanic Sciences, University of Colorado, Boulder, Colorado 80309, USA
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28
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Mizuta A, Matsumoto T, Toh S. Transition of the scaling law in inverse energy cascade range caused by a nonlocal excitation of coherent structures observed in two-dimensional turbulent fields. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:053009. [PMID: 24329353 DOI: 10.1103/physreve.88.053009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2013] [Revised: 08/25/2013] [Indexed: 06/03/2023]
Abstract
We numerically investigate the inverse energy cascade range of two-dimensional Navier-Stokes turbulence. Our focus is on the universality of the Kolmogorov's phenomenology. In our direct numerical simulations, two types of forcing processes, the random forcing and the deterministic forcing, are employed besides the systematically varied numerical parameters. We first calculate the two-dimensional Navier-Stokes equations and confirm that results in the quasi steady state are consistent with the classical phenomenology for both types of forcing processes. It is also found that the difference in forcing process appears after the inverse energy cascade range reaches the system size; the dipole coherent vortices emerge and grow only when the random forcing is adopted. Then we add a large-scale drag term to the Navier-Stokes equations to obtain the statistically stationary state. When the random forcing is used, the scaling exponent of the energy spectrum in the stationary state starts to differ from the predicted -5/3 in the inverse energy cascade range as the infrared Reynolds number Re(d) increases, where Re(d) is defined as k(f)/k(d) with the forcing wave number k(f) and the large-scale drag wave number k(d). That can be interpreted as a transition phenomenon in which the local maximum vorticity grows like an order parameter caused by excitation of strong coherent vortices. Strong coherent vortices emerge and grow after the quasi steady state and destroy the scaling law when Re(d) is over a critical value. These coherent vortices are not due to the finite-size effect, unlike the dipole coherent vortices. On the other hand, when the deterministic forcing is adopted, strong coherent vortices are hardly seen and the -5/3 scaling law holds independently of Re(d). We examine the cases of the combination of both types of forcing processes and find that formation of such coherent vortices is sensitive to the mechanism of the external forcing process as well as the numerical parameters. Several types of large-scale drag terms are also tested and their insignificant influence on these qualitative properties is revealed.
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Affiliation(s)
- Atsushi Mizuta
- Software Cradle Co., Ltd., 3-4-5, Umeda, Kita-ku Osaka, Japan and Division of Physics and Astronomy, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Takeshi Matsumoto
- Division of Physics and Astronomy, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Sadayoshi Toh
- Division of Physics and Astronomy, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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29
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Miller P, Vladimirova N, Falkovich G. Oscillations in a turbulence-condensate system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:065202. [PMID: 23848817 DOI: 10.1103/physreve.87.065202] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/25/2013] [Revised: 05/14/2013] [Indexed: 06/02/2023]
Abstract
We consider developed turbulence in the Gross-Pitaevsky model, where a condensate appears due to an inverse cascade. Despite being fully turbulent, the system demonstrates nondecaying periodic oscillations around a steady state, when turbulence and condensate periodically exchange a small fraction of waves. We show that these collective oscillations are not of a predator-prey type, as was suggested earlier; rather, they are due to phase coherence and anomalous correlations imposed by the condensate.
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Affiliation(s)
- Pearson Miller
- Yale University, Department of Physics, New Haven, Connecticut 06511, USA
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30
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Reeves MT, Billam TP, Anderson BP, Bradley AS. Inverse energy cascade in forced two-dimensional quantum turbulence. PHYSICAL REVIEW LETTERS 2013; 110:104501. [PMID: 23521262 DOI: 10.1103/physrevlett.110.104501] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2012] [Indexed: 06/01/2023]
Abstract
We demonstrate an inverse energy cascade in a minimal model of forced 2D quantum vortex turbulence. We simulate the Gross-Pitaevskii equation for a moving superfluid subject to forcing by a stationary grid of obstacle potentials, and damping by a stationary thermal cloud. The forcing injects large amounts of vortex energy into the system at the scale of a few healing lengths. A regime of forcing and damping is identified where vortex energy is efficiently transported to large length scales via an inverse energy cascade associated with the growth of clusters of same-circulation vortices, a Kolmogorov scaling law in the kinetic energy spectrum over a substantial inertial range, and spectral condensation of kinetic energy at the scale of the system size. Our results provide clear evidence that the inverse energy cascade phenomenon, previously observed in a diverse range of classical systems, can also occur in quantum fluids.
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Affiliation(s)
- Matthew T Reeves
- Jack Dodd Centre for Quantum Technology, Department of Physics, University of Otago, Dunedin 9016, New Zealand
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31
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Chan CK, Mitra D, Brandenburg A. Dynamics of saturated energy condensation in two-dimensional turbulence. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:036315. [PMID: 22587188 DOI: 10.1103/physreve.85.036315] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/02/2011] [Revised: 02/02/2012] [Indexed: 05/31/2023]
Abstract
In two-dimensional forced Navier-Stokes turbulence, energy cascades to the largest scales in the system to form a pair of coherent vortices known as the Bose condensate. We show, both numerically and analytically, that the energy condensation saturates and the system reaches a statistically stationary state. The time scale of saturation is inversely proportional to the viscosity and the saturation energy level is determined by both the viscosity and the force. We further show that, without sufficient resolution to resolve the small-scale enstrophy spectrum, numerical simulations can give a spurious result for the saturation energy level. We also find that the movement of the condensate is similar to the motion of an inertial particle with an effective drag force. Furthermore, we show that the profile of the saturated coherent vortices can be described by a Gaussian core with exponential wings.
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Affiliation(s)
- Chi-kwan Chan
- NORDITA, Roslagstullsbacken 23, SE-10691, Stockholm, Sweden.
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32
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Vladimirova N, Derevyanko S, Falkovich G. Phase transitions in wave turbulence. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:010101. [PMID: 22400497 DOI: 10.1103/physreve.85.010101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2011] [Revised: 10/26/2011] [Indexed: 05/31/2023]
Abstract
We consider turbulence within the Gross-Pitaevsky model and look into the creation of a coherent condensate via an inverse cascade originating at small scales. The growth of the condensate leads to a spontaneous breakdown of statistical symmetries of overcondensate fluctuations: First, isotropy is broken, then a series of phase transitions marks the changing symmetry from twofold to threefold to fourfold. We describe respective anisotropic flux flows in the k space. At the highest level reached, we observe a short-range positional and long-range orientational order (as in a hexatic phase). In other words, the more one pumps the system, the more ordered the system becomes. The phase transitions happen when the system is pumped by an instability term and does not occur when pumped by a random force. We thus demonstrate nonuniversality of an inverse-cascade turbulence with respect to the nature of small-scale forcing.
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33
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Chertkov M, Kolokolov I, Lebedev V. Universal velocity profile for coherent vortices in two-dimensional turbulence. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:015302. [PMID: 20365424 DOI: 10.1103/physreve.81.015302] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2009] [Revised: 10/30/2009] [Indexed: 05/29/2023]
Abstract
Two-dimensional turbulence generated in a finite box produces large-scale coherent vortices coexisting with small-scale fluctuations. We present a rigorous theory explaining the eta=1/4 scaling in the V is proportional to r(-eta) law of the velocity spatial profile within a vortex, where r is the distance from the vortex center. This scaling, consistent with earlier numerical and laboratory measurements, is universal in its independence of details of the small-scale injection of turbulent fluctuations and details of the shape of the box.
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Affiliation(s)
- M Chertkov
- Center for Nonlinear Studies & Theoretical Division, LANL, Los Alamos, New Mexico 87545, USA
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34
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Bouchet F, Simonnet E. Random changes of flow topology in two-dimensional and geophysical turbulence. PHYSICAL REVIEW LETTERS 2009; 102:094504. [PMID: 19392527 DOI: 10.1103/physrevlett.102.094504] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2008] [Indexed: 05/27/2023]
Abstract
We study the two-dimensional (2D) stochastic Navier-Stokes (SNS) equations in the inertial limit of weak forcing and dissipation. The stationary measure is concentrated close to steady solutions of the 2D Euler equations. For such inertial flows, we prove that bifurcations in the flow topology occur either by changing the domain shape, the nonlinearity of the vorticity-stream-function relation, or the energy. Associated with this, we observe bistable behavior in SNS with random changes from dipoles to unidirectional flows. The theoretical explanation being very general, we infer the existence of similar phenomena in experiments and in some regimes of geophysical flows.
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Affiliation(s)
- Freddy Bouchet
- INLN, CNRS, UNSA, 1361 route des lucioles, 06560 Valbonne, France.
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35
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Xia H, Punzmann H, Falkovich G, Shats MG. Turbulence-condensate interaction in two dimensions. PHYSICAL REVIEW LETTERS 2008; 101:194504. [PMID: 19113273 DOI: 10.1103/physrevlett.101.194504] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2008] [Indexed: 05/27/2023]
Abstract
We present experimental results on turbulence generated in thin fluid layers in the presence of a large-scale coherent flow, or a spectral condensate. It is shown that the condensate modifies the third-order velocity moment in a much wider interval of scales than the second one. The modification may include the change of sign of the third moment in the inverse cascade. This observation may help resolve a controversy on the energy flux in mesoscale atmospheric turbulence (10-500 km): to recover a correct energy flux from the third velocity moment one needs first to subtract the coherent flow. We find that the condensate also increases the velocity flatness.
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Affiliation(s)
- H Xia
- Physical Sciences and Engineering, Australian National University, Canberra ACT 0200, Australia
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36
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Korotkevich AO. Simultaneous numerical simulation of direct and inverse cascades in wave turbulence. PHYSICAL REVIEW LETTERS 2008; 101:074504. [PMID: 18764542 DOI: 10.1103/physrevlett.101.074504] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2008] [Indexed: 05/26/2023]
Abstract
The results of the direct numerical simulation of isotropic turbulence of surface gravity waves in the framework of Hamiltonian equations are presented. For the first time, the simultaneous formation of both direct and inverse cascades has been observed in the framework of the primordial dynamical equations. At the same time, a strong long wave background has been developed. It has been shown that the Kolmogorov spectra obtained are very sensitive to the presence of this condensate. Such a situation has to be typical for experimental wave tanks, flumes, and small lakes.
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Affiliation(s)
- A O Korotkevich
- L. D. Landau Institute for Theoretical Physics RAS, 2 Kosygin Street, Moscow, 119334, Russian Federation.
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37
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Ganshin AN, Efimov VB, Kolmakov GV, Mezhov-Deglin LP, McClintock PVE. Observation of an inverse energy cascade in developed acoustic turbulence in superfluid helium. PHYSICAL REVIEW LETTERS 2008; 101:065303. [PMID: 18764469 DOI: 10.1103/physrevlett.101.065303] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2008] [Indexed: 05/26/2023]
Abstract
We report observation of an inverse energy cascade in second sound acoustic turbulence in He II. Its onset occurs above a critical driving energy and it is accompanied by giant waves that constitute an acoustic analogue of the rogue waves that occasionally appear on the surface of the ocean. The theory of the phenomenon is developed and shown to be in good agreement with the experiments.
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Affiliation(s)
- A N Ganshin
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, United Kingdom
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38
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Shats MG, Xia H, Punzmann H, Falkovich G. Suppression of turbulence by self-generated and imposed mean flows. PHYSICAL REVIEW LETTERS 2007; 99:164502. [PMID: 17995257 DOI: 10.1103/physrevlett.99.164502] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2007] [Indexed: 05/25/2023]
Abstract
The first direct experimental evidence of the suppression of quasi-two-dimensional turbulence by mean flows is presented. The flow either is induced externally or appears in the process of spectral condensation due to an inverse cascade in bounded turbulence. The observed suppression of large scales is consistent with an expected reduction in the correlation time of turbulent eddies due to shearing. At high flow velocities, sweeping of the forcing-scale vortices reduces the energy input, leading to a reduction in the turbulence level.
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Affiliation(s)
- M G Shats
- Plasma Research Laboratory, Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT 0200, Australia.
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