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Title: 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 » 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.« less

Authors:
 [1];  [2];  [3];  [4];  [5];  [5]
  1. Centre National de la Recherche Scientifique (CNRS), Paris (France). Lab. de Physique Statistique de l'École Normale Supérieure
  2. Univ. College Dublin, Dublin (Ireland). School of Mathematical Sciences
  3. Centre National de la Recherche Scientifique (CNRS), Paris (France)
  4. National Center for Atmospheric Research, Boulder, CO (United States). Computational and Information Systems Lab.; Univ. of Buenos Aires (Argentina). Dept. de Física
  5. 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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