Ideal evolution of magnetohydrodynamic turbulence when imposing Taylor-Green symmetries
Abstract
We investigate the ideal and incompressible magnetohydrodynamic (MHD) equations in three space dimensions for the development of potentially singular structures. The methodology consists in implementing the fourfold symmetries of the Taylor-Green vortex generalized to MHD, leading to substantial computer time and memory savings at a given resolution; we also use a regridding method that allows for lower-resolution runs at early times, with no loss of spectral accuracy. One magnetic configuration is examined at an equivalent resolution of $6144^3$ points and three different configurations on grids of $4096^3$ points. At the highest resolution, two different current and vorticity sheet systems are found to collide, producing two successive accelerations in the development of small scales. At the latest time, a convergence of magnetic field lines to the location of maximum current is probably leading locally to a strong bending and directional variability of such lines. A novel analytical method, based on sharp analysis inequalities, is used to assess the validity of the finite-time singularity scenario. This method allows one to rule out spurious singularities by evaluating the rate at which the logarithmic decrement of the analyticity-strip method goes to zero. The result is that the finite-time singularity scenario cannot be ruled out,more »
- Authors:
-
- Centre National de la Recherche Scientifique (CNRS), Paris (France). Lab. de Physique Statistique de l'École Normale Supérieure
- Univ. College Dublin, Dublin (Ireland). School of Mathematical Sciences
- Centre National de la Recherche Scientifique (CNRS), Paris (France)
- National Center for Atmospheric Research, Boulder, CO (United States). Computational and Information Systems Lab.; Univ. of Buenos Aires (Argentina). Dept. de Física
- National Center for Atmospheric Research, Boulder, CO (United States). Computational and Information Systems Lab.
- Publication Date:
- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1565059
- Alternate Identifier(s):
- OSTI ID: 1101982
- Grant/Contract Number:
- AC05-00OR22725
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
- Additional Journal Information:
- Journal Volume: 87; Journal Issue: 1; Journal ID: ISSN 1539-3755
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics
Citation Formats
Brachet, M. E., Bustamante, M. D., Krstulovic, G., Mininni, P. D., Pouquet, A., and Rosenberg, D. Ideal evolution of magnetohydrodynamic turbulence when imposing Taylor-Green symmetries. United States: N. p., 2013.
Web. doi:10.1103/physreve.87.013110.
Brachet, M. E., Bustamante, M. D., Krstulovic, G., Mininni, P. D., Pouquet, A., & Rosenberg, D. Ideal evolution of magnetohydrodynamic turbulence when imposing Taylor-Green symmetries. United States. doi:10.1103/physreve.87.013110.
Brachet, M. E., Bustamante, M. D., Krstulovic, G., Mininni, P. D., Pouquet, A., and Rosenberg, D. Wed .
"Ideal evolution of magnetohydrodynamic turbulence when imposing Taylor-Green symmetries". United States. doi:10.1103/physreve.87.013110. https://www.osti.gov/servlets/purl/1565059.
@article{osti_1565059,
title = {Ideal evolution of magnetohydrodynamic turbulence when imposing Taylor-Green symmetries},
author = {Brachet, M. E. and Bustamante, M. D. and Krstulovic, G. and Mininni, P. D. and Pouquet, A. and Rosenberg, D.},
abstractNote = {We investigate the ideal and incompressible magnetohydrodynamic (MHD) equations in three space dimensions for the development of potentially singular structures. The methodology consists in implementing the fourfold symmetries of the Taylor-Green vortex generalized to MHD, leading to substantial computer time and memory savings at a given resolution; we also use a regridding method that allows for lower-resolution runs at early times, with no loss of spectral accuracy. One magnetic configuration is examined at an equivalent resolution of $6144^3$ points and three different configurations on grids of $4096^3$ points. At the highest resolution, two different current and vorticity sheet systems are found to collide, producing two successive accelerations in the development of small scales. At the latest time, a convergence of magnetic field lines to the location of maximum current is probably leading locally to a strong bending and directional variability of such lines. A novel analytical method, based on sharp analysis inequalities, is used to assess the validity of the finite-time singularity scenario. This method allows one to rule out spurious singularities by evaluating the rate at which the logarithmic decrement of the analyticity-strip method goes to zero. The result is that the finite-time singularity scenario cannot be ruled out, and the singularity time could be somewhere between $t = 2.33$ and $t = 2.70$. More robust conclusions will require higher resolution runs and grid-point interpolation measurements of maximum current and vorticity.},
doi = {10.1103/physreve.87.013110},
journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics},
number = 1,
volume = 87,
place = {United States},
year = {2013},
month = {1}
}
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Works referenced in this record:
Effective Dissipation and Turbulence in Spectrally Truncated Euler Flows
journal, December 2005
- Cichowlas, Cyril; Bonaïti, Pauline; Debbasch, Fabrice
- Physical Review Letters, Vol. 95, Issue 26
Long-time properties of magnetohydrodynamic turbulence and the role of symmetries
journal, September 2012
- Stawarz, Julia E.; Pouquet, Annick; Brachet, Marc-Etienne
- Physical Review E, Vol. 86, Issue 3
Inertial ranges and resistive instabilities in two‐dimensional magnetohydrodynamic turbulence
journal, December 1989
- Politano, H.; Pouquet, A.; Sulem, P. L.
- Physics of Fluids B: Plasma Physics, Vol. 1, Issue 12
Transport of solar wind into Earth's magnetosphere through rolled-up Kelvin–Helmholtz vortices
journal, August 2004
- Hasegawa, H.; Fujimoto, M.; Phan, T. -D.
- Nature, Vol. 430, Issue 7001
Local interaction between vorticity and shear in a perfect incompressible fluid
journal, January 1982
- Vieillefosse, P.
- Journal de Physique, Vol. 43, Issue 6
Evidence for a singularity of the three‐dimensional, incompressible Euler equations
journal, July 1993
- Kerr, Robert M.
- Physics of Fluids A: Fluid Dynamics, Vol. 5, Issue 7
Singular, weak and absent: Solutions of the Euler equations
journal, August 2008
- Constantin, Peter
- Physica D: Nonlinear Phenomena, Vol. 237, Issue 14-17
A Sparse-Mode Spectral Method for the Simulation of Turbulent Flows
journal, January 1996
- Meneguzzi, M.; Politano, H.; Pouquet, A.
- Journal of Computational Physics, Vol. 123, Issue 1
Flow visualization and field line advection in computational fluid dynamics: application to magnetic fields and turbulent flows
journal, December 2008
- Mininni, Pablo; Lee, Ed; Norton, Alan
- New Journal of Physics, Vol. 10, Issue 12
Three-Dimensional Periodic Flows with High-Symmetry
journal, June 1985
- Kida, Shigeo
- Journal of the Physical Society of Japan, Vol. 54, Issue 6
Alfvén waves and ideal two-dimensional Galerkin truncated magnetohydrodynamics
journal, July 2011
- Krstulovic, Giorgio; Brachet, Marc-Etienne; Pouquet, Annick
- Physical Review E, Vol. 84, Issue 1
Finite dissipation and intermittency in magnetohydrodynamics
journal, August 2009
- Mininni, P. D.; Pouquet, A.
- Physical Review E, Vol. 80, Issue 2
A hybrid MPI–OpenMP scheme for scalable parallel pseudospectral computations for fluid turbulence
journal, June 2011
- Mininni, Pablo D.; Rosenberg, Duane; Reddy, Raghu
- Parallel Computing, Vol. 37, Issue 6-7
Euler equations for incompressible ideal fluids
journal, June 2007
- Bardos, Claude; Titi, Edriss
- Russian Mathematical Surveys, Vol. 62, Issue 3
High-Reynolds-number simulation of turbulent mixing
journal, August 2005
- Yeung, P. K.; Donzis, D. A.; Sreenivasan, K. R.
- Physics of Fluids, Vol. 17, Issue 8
Possibility of an inverse cascade of magnetic helicity in magnetohydrodynamic turbulence
journal, April 1975
- Frisch, U.; Pouquet, A.; LÉOrat, J.
- Journal of Fluid Mechanics, Vol. 68, Issue 4
Direct numerical simulation of transition to turbulence from a high‐symmetry initial condition
journal, August 1994
- Boratav, Oluş N.; Pelz, Richard B.
- Physics of Fluids, Vol. 6, Issue 8
Interactive desktop analysis of high resolution simulations: application to turbulent plume dynamics and current sheet formation
journal, August 2007
- Clyne, John; Mininni, Pablo; Norton, Alan
- New Journal of Physics, Vol. 9, Issue 8
Cascades, thermalization, and eddy viscosity in helical Galerkin truncated Euler flows
journal, May 2009
- Krstulovic, G.; Mininni, P. D.; Brachet, M. E.
- Physical Review E, Vol. 79, Issue 5
Large-scale flow effects, energy transfer, and self-similarity on turbulence
journal, July 2006
- Mininni, P. D.; Alexakis, A.; Pouquet, A.
- Physical Review E, Vol. 74, Issue 1
3D Euler equations and ideal MHD mapped to regular systems: Probing the finite-time blowup hypothesis
journal, June 2011
- Bustamante, Miguel D.
- Physica D: Nonlinear Phenomena, Vol. 240, Issue 13
Numerical simulations of possible finite time singularities in the incompressible Euler equations: Comparison of numerical methods
journal, August 2008
- Grafke, Tobias; Homann, Holger; Dreher, Jürgen
- Physica D: Nonlinear Phenomena, Vol. 237, Issue 14-17
Remarks on the breakdown of smooth solutions for the 3-D Euler equations
journal, March 1984
- Beale, J. T.; Kato, T.; Majda, A.
- Communications in Mathematical Physics, Vol. 94, Issue 1
Measurement of the rugged invariants of magnetohydrodynamic turbulence in the solar wind
journal, January 1982
- Matthaeus, William H.; Goldstein, Melvyn L.
- Journal of Geophysical Research, Vol. 87, Issue A8
A weak turbulence theory for incompressible magnetohydrodynamics
journal, June 2000
- Galtier, S.; Nazarenko, S. V.; Newell, A. C.
- Journal of Plasma Physics, Vol. 63, Issue 5
Turbulence Regimes and Turbulence Intermittency in the Stable Boundary Layer during CASES-99
journal, January 2012
- Sun, Jielun; Mahrt, Larry; Banta, Robert M.
- Journal of the Atmospheric Sciences, Vol. 69, Issue 1
Anisotropic Turbulence of Shear-Alfvén Waves
journal, January 2002
- Galtier, S.; Nazarenko, S. V.; Newell, A. C.
- The Astrophysical Journal, Vol. 564, Issue 1
Geophysical–astrophysical spectral-element adaptive refinement (GASpAR): Object-oriented h-adaptive fluid dynamics simulation
journal, June 2006
- Rosenberg, Duane; Fournier, Aimé; Fischer, Paul
- Journal of Computational Physics, Vol. 215, Issue 1
3D Euler about a 2D symmetry plane
journal, August 2008
- Bustamante, Miguel D.; Kerr, Robert M.
- Physica D: Nonlinear Phenomena, Vol. 237, Issue 14-17
Adaptive mesh refinement with spectral accuracy for magnetohydrodynamics in two space dimensions
journal, August 2007
- Rosenberg, D.; Pouquet, A.; Mininni, P. D.
- New Journal of Physics, Vol. 9, Issue 8
Blowup or no blowup? The interplay between theory and numerics
journal, August 2008
- Hou, Thomas Y.; Li, Ruo
- Physica D: Nonlinear Phenomena, Vol. 237, Issue 14-17
Interplay between the Beale-Kato-Majda theorem and the analyticity-strip method to investigate numerically the incompressible Euler singularity problem
journal, December 2012
- Bustamante, Miguel D.; Brachet, Marc
- Physical Review E, Vol. 86, Issue 6
Evidence for a Singularity in Ideal Magnetohydrodynamics: Implications for Fast Reconnection
journal, August 1999
- Kerr, Robert M.; Brandenburg, Axel
- Physical Review Letters, Vol. 83, Issue 6
Numerical evidence of smooth self‐similar dynamics and possibility of subsequent collapse for three‐dimensional ideal flows
journal, December 1992
- Brachet, M. E.; Meneguzzi, M.; Vincent, A.
- Physics of Fluids A: Fluid Dynamics, Vol. 4, Issue 12
Remarks on Singularities, Dimension and Energy Dissipation for Ideal Hydrodynamics and MHD
journal, April 1997
- Caflisch, Russel E.; Klapper, Isaac; Steele, Gregory
- Communications in Mathematical Physics, Vol. 184, Issue 2
A magnetic reconnection X-line extending more than 390 Earth radii in the solar wind
journal, January 2006
- Phan, T. D.; Gosling, J. T.; Davis, M. S.
- Nature, Vol. 439, Issue 7073
Small-Scale Structures in Three-Dimensional Magnetohydrodynamic Turbulence
journal, December 2006
- Mininni, P. D.; Pouquet, A. G.; Montgomery, D. C.
- Physical Review Letters, Vol. 97, Issue 24
The three-dimensional Euler equations: Where do we stand?
journal, August 2008
- Gibbon, J. D.
- Physica D: Nonlinear Phenomena, Vol. 237, Issue 14-17
Geometric Statistics in Turbulence
journal, March 1994
- Constantin, Peter
- SIAM Review, Vol. 36, Issue 1
Intermittency in MHD turbulence and coronal nanoflares modelling
journal, January 2005
- Veltri, P.; Nigro, G.; Malara, F.
- Nonlinear Processes in Geophysics, Vol. 12, Issue 2
Paradigmatic flow for small-scale magnetohydrodynamics: Properties of the ideal case and the collision of current sheets
journal, December 2008
- Lee, E.; Brachet, M. E.; Pouquet, A.
- Physical Review E, Vol. 78, Issue 6
A Lagrangian study of dynamics and singularity formation at magnetic null points in ideal three‐dimensional magnetohydrodynamics
journal, November 1996
- Klapper, I.; Rado, A.; Tabor, M.
- Physics of Plasmas, Vol. 3, Issue 11
Evolution of complex singularities in Kida–Pelz and Taylor–Green inviscid flows
journal, April 2005
- Cichowlas, C.; Brachet, M-E
- Fluid Dynamics Research, Vol. 36, Issue 4-6
Small-scale structure of the Taylor–Green vortex
journal, May 1983
- Brachet, Marc E.; Meiron, Daniel I.; Orszag, Steven A.
- Journal of Fluid Mechanics, Vol. 130, Issue -1
Depression of Nonlinearity in Decaying Isotropic MHD Turbulence
journal, March 2008
- Servidio, S.; Matthaeus, W. H.; Dmitruk, P.
- Physical Review Letters, Vol. 100, Issue 9
The size and dynamics of magnetic flux structures in magnetohydrodynamic turbulence
journal, April 1995
- Brandenburg, Axel; Procaccia, Itamar; Segel, Daniel
- Physics of Plasmas, Vol. 2, Issue 4
Rapid Alignment of Velocity and Magnetic Field in Magnetohydrodynamic Turbulence
journal, February 2008
- Matthaeus, W. H.; Pouquet, A.; Mininni, P. D.
- Physical Review Letters, Vol. 100, Issue 8
On Hydromagnetic Equilibrium
journal, September 1958
- Woltjer, L.
- Proceedings of the National Academy of Sciences, Vol. 44, Issue 9
Shell-to-shell energy transfer in magnetohydrodynamics. I. Steady state turbulence
journal, October 2005
- Alexakis, Alexandros; Mininni, Pablo D.; Pouquet, Annick
- Physical Review E, Vol. 72, Issue 4
Current sheet formation in two-dimensional incompressible MHD turbulence from a lagrangian point of view
journal, December 1993
- Klapper, I.; Tabor, M.
- Geophysical & Astrophysical Fluid Dynamics, Vol. 73, Issue 1-4
Constraints on finite-time current sheet formation at null points in two-dimensional ideal incompressible magnetohydrodynamics
journal, April 1998
- Klapper, I.
- Physics of Plasmas, Vol. 5, Issue 4
Lack of universality in decaying magnetohydrodynamic turbulence
journal, January 2010
- Lee, E.; Brachet, M. E.; Pouquet, A.
- Physical Review E, Vol. 81, Issue 1
General introduction
journal, August 2008
- Eyink, Gregory; Frisch, Uriel; Moreau, René
- Physica D: Nonlinear Phenomena, Vol. 237, Issue 14-17
Adaptive Mesh Refinement for Singular Solutions of the Incompressible Euler Equations
journal, May 1998
- Grauer, Rainer; Marliani, Christiane; Germaschewski, Kai
- Physical Review Letters, Vol. 80, Issue 19
Shell-to-shell energy transfer in magnetohydrodynamics. II. Kinematic dynamo
journal, October 2005
- Mininni, Pablo; Alexakis, Alexandros; Pouquet, Annick
- Physical Review E, Vol. 72, Issue 4
Internal motion of a small element of fluid in an inviscid flow
journal, April 1984
- Vieillefosse, P.
- Physica A: Statistical Mechanics and its Applications, Vol. 125, Issue 1
Geometry of singular structures in magnetohydrodynamic flows
journal, July 1998
- Grauer, Rainer; Marliani, Christiane
- Physics of Plasmas, Vol. 5, Issue 7
Velocity and scaling of collapsing Euler vortices
journal, July 2005
- Kerr, Robert M.
- Physics of Fluids, Vol. 17, Issue 7
Simulation of vortex reconnection
journal, July 1989
- Kerr, Robert M.; Hussain, Fazle
- Physica D: Nonlinear Phenomena, Vol. 37, Issue 1-3
Creation and dynamics of vortex tubes in three-dimensional turbulence
journal, April 1995
- Constantin, Peter; Procaccia, Itamar; Segel, Daniel
- Physical Review E, Vol. 51, Issue 4
Current-Sheet Formation in 3D Ideal Incompressible Magnetohydrodynamics
journal, May 2000
- Grauer, Rainer; Marliani, Christiane
- Physical Review Letters, Vol. 84, Issue 21
On the validity of a nonlocal approach for MHD turbulence
journal, August 1999
- Gomez, T.; Politano, H.; Pouquet, A.
- Physics of Fluids, Vol. 11, Issue 8
The dynamics of unforced turbulence at high Reynolds number for Taylor–Green vortices generalized to MHD
journal, April 2010
- Pouquet, A.; Lee, E.; Brachet, M. E.
- Geophysical & Astrophysical Fluid Dynamics, Vol. 104, Issue 2-3
A possible generation mechanism of interplanetary rotational discontinuities: INTERPLANETARY ROTATIONAL DISCONTINUITY
journal, August 2009
- Lin, C. C.; Tsai, C. L.; Chen, H. J.
- Journal of Geophysical Research: Space Physics, Vol. 114, Issue A8
Symmetry and the hydrodynamic blow-up problem
journal, September 2001
- Pelz, Richard B.
- Journal of Fluid Mechanics, Vol. 444
Dynamic Depletion of Vortex Stretching and Non-Blowup of the 3-D Incompressible Euler Equations
journal, August 2006
- Hou, Thomas Y.; Li, Ruo
- Journal of Nonlinear Science, Vol. 16, Issue 6
MHD turbulence in the solar wind: self-similarity, intermittency and coherent structures
journal, January 1999
- Veltri, Pierluigi
- Plasma Physics and Controlled Fusion, Vol. 41, Issue 3A
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journal, July 2015
- Nigro, G.; Carbone, V.
- New Journal of Physics, Vol. 17, Issue 7
Evidence for Bolgiano-Obukhov scaling in rotating stratified turbulence using high-resolution direct numerical simulations
journal, May 2015
- Rosenberg, D.; Pouquet, A.; Marino, R.
- Physics of Fluids, Vol. 27, Issue 5
Generation of turbulence through frontogenesis in sheared stratified flows
journal, August 2018
- Sujovolsky, N. E.; Mininni, P. D.; Pouquet, A.
- Physics of Fluids, Vol. 30, Issue 8
Equilibria, Dynamics, and Current Sheet Formation in Magnetically Confined Coronae
journal, December 2015
- Rappazzo, A. F.
- The Astrophysical Journal, Vol. 815, Issue 1
Magnetic Reconnection: Recursive Current Sheet Collapse Triggered by “Ideal” Tearing
journal, November 2015
- Tenerani, Anna; Velli, Marco; Rappazzo, Antonio Franco
- The Astrophysical Journal, Vol. 813, Issue 2
Turbulent cascade, bottleneck, and thermalized spectrum in hyperviscous flows
journal, February 2020
- Agrawal, Rahul; Alexakis, Alexandros; Brachet, Marc E.
- Physical Review Fluids, Vol. 5, Issue 2
Coronal Heating Topology: The Interplay of Current Sheets and Magnetic Field Lines
journal, July 2017
- Rappazzo, A. F.; Matthaeus, W. H.; Ruffolo, D.
- The Astrophysical Journal, Vol. 844, Issue 1