Ideal evolution of magnetohydrodynamic turbulence when imposing Taylor-Green symmetries
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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paper:paper_15393755_v87_n1_p_Brachet2023-06-08T16:20:55Z Ideal evolution of magnetohydrodynamic turbulence when imposing Taylor-Green symmetries Mininni, Pablo Daniel 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 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v87_n1_p_Brachet 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) |
| 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 Mininni, Pablo Daniel 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. |
| author |
Mininni, Pablo Daniel |
| author_facet |
Mininni, Pablo Daniel |
| author_sort |
Mininni, Pablo Daniel |
| 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 |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v87_n1_p_Brachet http://hdl.handle.net/20.500.12110/paper_15393755_v87_n1_p_Brachet |
| work_keys_str_mv |
AT mininnipablodaniel idealevolutionofmagnetohydrodynamicturbulencewhenimposingtaylorgreensymmetries |
| _version_ |
1768544612794761216 |