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Agoua W, Favier B, Delache A, Briard A, Bos WJT. Spontaneous generation and reversal of helicity in anisotropic turbulence. Phys Rev E 2021; 103:L061101. [PMID: 34271682 DOI: 10.1103/physreve.103.l061101] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2020] [Accepted: 05/05/2021] [Indexed: 11/07/2022]
Abstract
Helicity plays an important role in spectacular geophysical phenomena such as hurricanes or the generation of the terrestrial magnetic field. The present investigation shows how helicity can be created in a statistically homogeneous but anisotropic flow, driven by buoyancy. If the flow is close enough to a two-dimensional limit, spontaneous symmetry breaking leads to the generation of mean helicity. In particular, we explain these observations by identifying a simple linear mechanism, the relevance of which is illustrated by simulations of unstably stratified turbulence in a conducting fluid on which a magnetic field is imposed. Finally it is shown that the self-organized state displays dynamical reversals of the sign of the mean helicity.
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Affiliation(s)
- Wesley Agoua
- CNRS, Univ Lyon, Ecole Centrale de Lyon, Univ Lyon 1 Claude Bernard, INSA Lyon, Laboratoire de Mécanique des Fluides et d'Acoustique, UMR5509, 69134 Ecully, France
| | - Benjamin Favier
- Aix Marseille Univ, CNRS, Centrale Marseille, IRPHE UMR 7342, Marseille, France
| | - Alexandre Delache
- CNRS, Univ Lyon, Ecole Centrale de Lyon, Univ Lyon 1 Claude Bernard, INSA Lyon, Laboratoire de Mécanique des Fluides et d'Acoustique, UMR5509, 69134 Ecully, France and Université Jean Monnet de Saint Etienne, 42000 Saint Etienne, France
| | | | - Wouter J T Bos
- CNRS, Univ Lyon, Ecole Centrale de Lyon, Univ Lyon 1 Claude Bernard, INSA Lyon, Laboratoire de Mécanique des Fluides et d'Acoustique, UMR5509, 69134 Ecully, France
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Maity P, Govindarajan R, Ray SS. Statistics of Lagrangian trajectories in a rotating turbulent flow. Phys Rev E 2019; 100:043110. [PMID: 31771019 DOI: 10.1103/physreve.100.043110] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2019] [Indexed: 11/07/2022]
Abstract
We investigate the Lagrangian statistics of three-dimensional rotating turbulent flows through direct numerical simulations. We find that the emergence of coherent vortical structures because of the Coriolis force leads to a suppression of the "flight-crash" events reported by Xu et al. [Proc. Natl. Acad. Sci. (USA) 111, 7558 (2014)PNASA60027-842410.1073/pnas.1321682111]. We perform systematic studies to trace the origins of this suppression in the emergent geometry of the flow and show why such a Lagrangian measure of irreversibility may fail in the presence of rotation.
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Affiliation(s)
- Priyanka Maity
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Hessaraghatta, Hobli, Bangalore 560089, India
| | - Rama Govindarajan
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Hessaraghatta, Hobli, Bangalore 560089, India
| | - Samriddhi Sankar Ray
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Hessaraghatta, Hobli, Bangalore 560089, India
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Rasskazov A, Chertovskih R, Zheligovsky V. Magnetic field generation by pointwise zero-helicity three-dimensional steady flow of an incompressible electrically conducting fluid. Phys Rev E 2018; 97:043201. [PMID: 29758748 DOI: 10.1103/physreve.97.043201] [Citation(s) in RCA: 34] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2017] [Indexed: 11/07/2022]
Abstract
We introduce six families of three-dimensional space-periodic steady solenoidal flows, whose kinetic helicity density is zero at any point. Four families are analytically defined. Flows in four families have zero helicity spectrum. Sample flows from five families are used to demonstrate numerically that neither zero kinetic helicity density nor zero helicity spectrum prohibit generation of large-scale magnetic field by the two most prominent dynamo mechanisms: the magnetic α-effect and negative eddy diffusivity. Our computations also attest that such flows often generate small-scale field for sufficiently small magnetic molecular diffusivity. These findings indicate that kinetic helicity and helicity spectrum are not the quantities controlling the dynamo properties of a flow regardless of whether scale separation is present or not.
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Affiliation(s)
- Andrey Rasskazov
- Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences, 84/32 Profsoyuznaya Street, 117997 Moscow, Russian Federation
| | - Roman Chertovskih
- Research Center for Systems and Technologies (SYSTEC), Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal.,Samara National Research University, 34 Moskovskoye Avenue, 443086 Samara, Russian Federation
| | - Vladislav Zheligovsky
- Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences, 84/32 Profsoyuznaya Street, 117997 Moscow, Russian Federation
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Imazio PR, Mininni PD. Passive scalars: Mixing, diffusion, and intermittency in helical and nonhelical rotating turbulence. Phys Rev E 2017; 95:033103. [PMID: 28415185 DOI: 10.1103/physreve.95.033103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2015] [Indexed: 06/07/2023]
Abstract
We use direct numerical simulations to compute structure functions, scaling exponents, probability density functions, and effective transport coefficients of passive scalars in turbulent rotating helical and nonhelical flows. We show that helicity affects the inertial range scaling of the velocity and of the passive scalar when rotation is present, with a spectral law consistent with ∼k_{⊥}^{-1.4} for the passive scalar variance spectrum. This scaling law is consistent with a phenomenological argument [P. Rodriguez Imazio and P. D. Mininni, Phys. Rev. E 83, 066309 (2011)PLEEE81539-375510.1103/PhysRevE.83.066309] for rotating nonhelical flows, which follows directly from Kolmogorov-Obukhov scaling and states that if energy follows a E(k)∼k^{-n} law, then the passive scalar variance follows a law V(k)∼k^{-n_{θ}} with n_{θ}=(5-n)/2. With the second-order scaling exponent obtained from this law, and using the Kraichnan model, we obtain anomalous scaling exponents for the passive scalar that are in good agreement with the numerical results. Multifractal intermittency models are also considered. Intermittency of the passive scalar is stronger than in the nonhelical rotating case, a result that is also confirmed by stronger non-Gaussian tails in the probability density functions of field increments. Finally, Fick's law is used to compute the effective diffusion coefficients in the directions parallel and perpendicular to rotation. Calculations indicate that horizontal diffusion decreases in the presence of helicity in rotating flows, while vertical diffusion increases. A simple mean field argument explains this behavior in terms of the amplitude of velocity fluctuations.
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Affiliation(s)
- P Rodriguez Imazio
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IFIBA, CONICET, Cuidad Universitaria, Buenos Aires 1428, Argentina
- Laboratoire de Physique Statistique, Ecole Normale Supérieure, CNRS, 24 rue Lhomond, 75005 Paris, France
| | - P D Mininni
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IFIBA, CONICET, Cuidad Universitaria, Buenos Aires 1428, Argentina
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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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Galtier S. Theory for helical turbulence under fast rotation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:041001. [PMID: 24827177 DOI: 10.1103/physreve.89.041001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/31/2013] [Indexed: 06/03/2023]
Abstract
Recent numerical simulations have shown the strong impact of helicity on homogeneous rotating hydrodynamic turbulence. The main effect can be summarized through the law n+ñ=-4, where n and ñ are the power law indices of the one-dimensional energy and helicity spectra, respectively. We investigate this rotating turbulence problem in the small Rossby number limit by using the asymptotic weak turbulence theory derived previously. We show that the empirical law is an exact solution of the helicity equation where the power law indices correspond to perpendicular (to the rotation axis) wave number spectra. It is proposed that when the cascade towards small scales tends to be dominated by the helicity flux the solution tends to ñ=-2, whereas it is ñ=-3/2 when the energy flux dominates. The latter is compatible with the solution previously observed numerically and derived theoretically in the weak turbulence regime when only the energy equation is used, whereas the former solution is constrained by a locality condition.
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Affiliation(s)
- Sébastien Galtier
- Laboratoire de Physique des Plasmas, Ecole Polytechnique, F-91128 Palaiseau Cedex, France
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Rorai C, Rosenberg D, Pouquet A, Mininni PD. Helicity dynamics in stratified turbulence in the absence of forcing. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:063007. [PMID: 23848772 DOI: 10.1103/physreve.87.063007] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/27/2012] [Revised: 03/05/2013] [Indexed: 05/20/2023]
Abstract
A numerical study of decaying stably stratified flows is performed. Relatively high stratification (Froude number ≈10(-2)-10(-1)) and moderate Reynolds (Re) numbers (Re≈ 3-6×10(3)) are considered and a particular emphasis is placed on the role of helicity (velocity-vorticity correlations), which is not an invariant of the nondissipative equations. The problem is tackled by integrating the Boussinesq equations in a periodic cubical domain using different initial conditions: a nonhelical Taylor-Green (TG) flow, a fully helical Beltrami [Arnold-Beltrami-Childress (ABC)] flow, and random flows with a tunable helicity. We show that for stratified ABC flows helicity undergoes a substantially slower decay than for unstratified ABC flows. This fact is likely associated to the combined effect of stratification and large-scale coherent structures. Indeed, when the latter are missing, as in random flows, helicity is rapidly destroyed by the onset of gravitational waves. A type of large-scale dissipative "cyclostrophic" balance can be invoked to explain this behavior. No production of helicity is observed, contrary to the case of rotating and stratified flows. When helicity survives in the system, it strongly affects the temporal energy decay and the energy distribution among Fourier modes. We discover in fact that the decay rate of energy for stratified helical flows is much slower than for stratified nonhelical flows and can be considered with a phenomenological model in a way similar to what is done for unstratified rotating flows. We also show that helicity, when strong, has a measurable effect on the Fourier spectra, in particular at scales larger than the buoyancy scale, for which it displays a rather flat scaling associated with vertical shear, as observed in the planetary boundary layer.
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Affiliation(s)
- C Rorai
- National Center for Atmospheric Research, P. O. Box 3000, Boulder, Colorado 80307, USA
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Sen A, Mininni PD, Rosenberg D, Pouquet A. Anisotropy and nonuniversality in scaling laws of the large-scale energy spectrum in rotating turbulence. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:036319. [PMID: 23031025 DOI: 10.1103/physreve.86.036319] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2012] [Indexed: 06/01/2023]
Abstract
Rapidly rotating turbulent flow is characterized by the emergence of columnar structures that are representative of quasi-two-dimensional behavior of the flow. It is known that when energy is injected into the fluid at an intermediate scale Lf, it cascades towards smaller as well as larger scales. In this paper we analyze the flow in the inverse cascade range at a small but fixed Rossby number, Rof≈0.05. Several numerical simulations with helical and nonhelical forcing functions are considered in periodic boxes with unit aspect ratio. In order to resolve the inverse cascade range with reasonably large Reynolds number, the analysis is based on large eddy simulations which include the effect of helicity on eddy viscosity and eddy noise. Thus, we model the small scales and resolve explicitly the large scales. We show that the large-scale energy spectrum has at least two solutions: one that is consistent with Kolmogorov-Kraichnan-Batchelor-Leith phenomenology for the inverse cascade of energy in two-dimensional (2D) turbulence with a ∼k⊥-5/3 scaling, and the other that corresponds to a steeper ∼k⊥-3 spectrum in which the three-dimensional (3D) modes release a substantial fraction of their energy per unit time to the 2D modes. The spectrum that emerges depends on the anisotropy of the forcing function, the former solution prevailing for forcings in which more energy is injected into the 2D modes while the latter prevails for isotropic forcing. In the case of anisotropic forcing, whence the energy goes from the 2D to the 3D modes at low wave numbers, large-scale shear is created, resulting in a time scale τsh, associated with shear, thereby producing a ∼k-1 spectrum for the total energy with the horizontal energy of the 2D modes still following a ∼k⊥-5/3 scaling.
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Affiliation(s)
- Amrik Sen
- Institute for Mathematics Applied to Geosciences, CISL, NCAR, P.O. Box 3000, Boulder, Colorado 80307-3000, USA
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Abarzhi SI, Sreenivasan KR. Turbulent mixing and beyond. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2010; 368:1539-1546. [PMID: 20211872 DOI: 10.1098/rsta.2010.0021] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
Turbulence is a supermixer. Turbulent mixing has immense consequences for physical phenomena spanning astrophysical to atomistic scales under both high- and low-energy-density conditions. It influences thermonuclear fusion in inertial and magnetic confinement systems; governs dynamics of supernovae, accretion disks and explosions; dominates stellar convection, planetary interiors and mantle-lithosphere tectonics; affects premixed and non-premixed combustion; controls standard turbulent flows (wall-bounded and free-subsonic, supersonic as well as hypersonic); as well as atmospheric and oceanic phenomena (which themselves have important effects on climate). In most of these circumstances, the mixing phenomena are driven by non-equilibrium dynamics. While each article in this collection dwells on a specific problem, the purpose here is to seek a few unified themes amongst diverse phenomena.
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Affiliation(s)
- S I Abarzhi
- Division of Physical Sciences and Department of Astronomy and Astrophysics, University of Chicago, Chicago, IL, USA
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