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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 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.

Registro:

Documento: Artículo
Título:Ideal evolution of magnetohydrodynamic turbulence when imposing Taylor-Green symmetries
Autor:Brachet, M.E.; Bustamante, M.D.; Krstulovic, G.; Mininni, P.D.; Pouquet, A.; Rosenberg, D.
Filiación:Laboratoire de Physique Statistique de l'École Normale Supérieure Associé, CNRS, Universités ParisVI et VII, 24 Rue Lhomond, 75231 Paris, France
School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland
Laboratoire Lagrange UMR7293, Université de Nice Sophia-Antipolis, CNRS, Observatoire de la Côte d'Azur, B.P. 4229, 06304 Nice Cedex 4, France
Computational and Information Systems Laboratory, NCAR, P. O. Box 3000, Boulder, CO 80307, United States
Departamento de Física, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Palabras clave: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
Año:2013
Volumen:87
Número:1
DOI: http://dx.doi.org/10.1103/PhysRevE.87.013110
Título revista:Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
Título revista abreviado:Phys. Rev. E Stat. Nonlinear Soft Matter Phys.
ISSN:15393755
CODEN:PLEEE
CAS:Plasma Gases
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_15393755_v87_n1_p_Brachet.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v87_n1_p_Brachet

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Citas:

---------- APA ----------
Brachet, M.E., Bustamante, M.D., Krstulovic, G., Mininni, P.D., Pouquet, A. & Rosenberg, D. (2013) . Ideal evolution of magnetohydrodynamic turbulence when imposing Taylor-Green symmetries. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 87(1).
http://dx.doi.org/10.1103/PhysRevE.87.013110
---------- CHICAGO ----------
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" . Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 87, no. 1 (2013).
http://dx.doi.org/10.1103/PhysRevE.87.013110
---------- MLA ----------
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" . Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, vol. 87, no. 1, 2013.
http://dx.doi.org/10.1103/PhysRevE.87.013110
---------- VANCOUVER ----------
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. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 2013;87(1).
http://dx.doi.org/10.1103/PhysRevE.87.013110