Ideal evolution of magnetohydrodynamic turbulence when imposing Taylor-Green symmetries

AMS Citation:
Brachet, M. E., M. D. Bustamante, G. Krstulovic, P. D. Mininni, A. Pouquet, and D. L. Rosenberg, 2013: Ideal evolution of magnetohydrodynamic turbulence when imposing Taylor-Green symmetries. Physical Review E, 87, 14 pp, doi:10.1103/PhysRevE.87.013110.
Resource Type:article
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 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.
Peer Review:Refereed
Copyright Information:Copyright 2013 American Physical Society.
OpenSky citable URL: ark:/85065/d7p26zzf
Publisher's Version: 10.1103/PhysRevE.87.013110
  • M. Brachet
  • M. Bustamante
  • G. Krstulovic
  • Pablo Mininni - NCAR/UCAR
  • Annick Pouquet - NCAR/UCAR
  • Duane Rosenberg - NCAR/UCAR
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