Ideal evolution of magnetohydrodynamic turbulence when imposing Taylor-Green symmetries

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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 com...

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Autores principales: Brachet, M.E., Bustamante, M.D., Krstulovic, G., Mininni, P.D., Pouquet, A., Rosenberg, D.
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: 2013
Materias:
Analytical method
Computer time
Finite time singularity
Four-fold symmetry
Higher resolution
Highest resolutions
Incompressible magnetohydrodynamics
Interpolation measurements
Logarithmic decrement
Magnetic configuration
Magnetic field line
Magnetohydrodynamic turbulence
Memory savings
Regridding
Singular structure
Small scale
Spectral accuracy
Taylor-Green vortex
Three space dimensions
Vorticity
Magnetohydrodynamics
algorithm
article
chemical model
chemistry
computer simulation
flow kinetics
hydrodynamics
magnetic field
methodology
nonlinear system
plasma gas
Algorithms
Computer Simulation
Hydrodynamics
Magnetic Fields
Models, Chemical
Nonlinear Dynamics
Plasma Gases
Rheology
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_15393755_v87_n1_p_Brachet
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paperaa:paper_15393755_v87_n1_p_Brachet
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spelling paperaa:paper_15393755_v87_n1_p_Brachet2023-06-12T16:50:42Z Ideal evolution of magnetohydrodynamic turbulence when imposing Taylor-Green symmetries Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 2013;87(1) Brachet, M.E. Bustamante, M.D. Krstulovic, G. Mininni, P.D. Pouquet, A. Rosenberg, D. Analytical method Computer time Finite time singularity Four-fold symmetry Higher resolution Highest resolutions Incompressible magnetohydrodynamics Interpolation measurements Logarithmic decrement Magnetic configuration Magnetic field line Magnetohydrodynamic turbulence Memory savings Regridding Singular structure Small scale Spectral accuracy Taylor-Green vortex Three space dimensions Vorticity Magnetohydrodynamics algorithm article chemical model chemistry computer simulation flow kinetics hydrodynamics magnetic field methodology nonlinear system plasma gas Algorithms Computer Simulation Hydrodynamics Magnetic Fields Models, Chemical Nonlinear Dynamics Plasma Gases Rheology 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 61443 points and three different configurations on grids of 40963 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. © 2013 American Physical Society. Fil:Mininni, P.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2013 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_15393755_v87_n1_p_Brachet
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language Inglés
orig_language_str_mv eng
topic Analytical method
Computer time
Finite time singularity
Four-fold symmetry
Higher resolution
Highest resolutions
Incompressible magnetohydrodynamics
Interpolation measurements
Logarithmic decrement
Magnetic configuration
Magnetic field line
Magnetohydrodynamic turbulence
Memory savings
Regridding
Singular structure
Small scale
Spectral accuracy
Taylor-Green vortex
Three space dimensions
Vorticity
Magnetohydrodynamics
algorithm
article
chemical model
chemistry
computer simulation
flow kinetics
hydrodynamics
magnetic field
methodology
nonlinear system
plasma gas
Algorithms
Computer Simulation
Hydrodynamics
Magnetic Fields
Models, Chemical
Nonlinear Dynamics
Plasma Gases
Rheology
spellingShingle Analytical method
Computer time
Finite time singularity
Four-fold symmetry
Higher resolution
Highest resolutions
Incompressible magnetohydrodynamics
Interpolation measurements
Logarithmic decrement
Magnetic configuration
Magnetic field line
Magnetohydrodynamic turbulence
Memory savings
Regridding
Singular structure
Small scale
Spectral accuracy
Taylor-Green vortex
Three space dimensions
Vorticity
Magnetohydrodynamics
algorithm
article
chemical model
chemistry
computer simulation
flow kinetics
hydrodynamics
magnetic field
methodology
nonlinear system
plasma gas
Algorithms
Computer Simulation
Hydrodynamics
Magnetic Fields
Models, Chemical
Nonlinear Dynamics
Plasma Gases
Rheology
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
topic_facet Analytical method
Computer time
Finite time singularity
Four-fold symmetry
Higher resolution
Highest resolutions
Incompressible magnetohydrodynamics
Interpolation measurements
Logarithmic decrement
Magnetic configuration
Magnetic field line
Magnetohydrodynamic turbulence
Memory savings
Regridding
Singular structure
Small scale
Spectral accuracy
Taylor-Green vortex
Three space dimensions
Vorticity
Magnetohydrodynamics
algorithm
article
chemical model
chemistry
computer simulation
flow kinetics
hydrodynamics
magnetic field
methodology
nonlinear system
plasma gas
Algorithms
Computer Simulation
Hydrodynamics
Magnetic Fields
Models, Chemical
Nonlinear Dynamics
Plasma Gases
Rheology
description 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 61443 points and three different configurations on grids of 40963 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. © 2013 American Physical Society.
format Artículo
Artículo
publishedVersion
author Brachet, M.E.
Bustamante, M.D.
Krstulovic, G.
Mininni, P.D.
Pouquet, A.
Rosenberg, D.
author_facet Brachet, M.E.
Bustamante, M.D.
Krstulovic, G.
Mininni, P.D.
Pouquet, A.
Rosenberg, D.
author_sort Brachet, M.E.
title Ideal evolution of magnetohydrodynamic turbulence when imposing Taylor-Green symmetries
title_short Ideal evolution of magnetohydrodynamic turbulence when imposing Taylor-Green symmetries
title_full Ideal evolution of magnetohydrodynamic turbulence when imposing Taylor-Green symmetries
title_fullStr Ideal evolution of magnetohydrodynamic turbulence when imposing Taylor-Green symmetries
title_full_unstemmed Ideal evolution of magnetohydrodynamic turbulence when imposing Taylor-Green symmetries
title_sort ideal evolution of magnetohydrodynamic turbulence when imposing taylor-green symmetries
publishDate 2013
url http://hdl.handle.net/20.500.12110/paper_15393755_v87_n1_p_Brachet
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