M. E. Brachet, M. D. Bustamante, G. Krstulovic, P. D. Mininni, A. Pouquet, D. Rosenberg
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 four-fold 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 re-gridding 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 ones on grids of 4096^3 points. We find that at the highest resolution, two different current and vorticity sheet systems collide, producing two successive accelerations in the development of small scales with, at the latest time, a convergence of magnetic field lines to the location of maximum current, probably leading locally to a strong bending and directional variability of such lines.
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http://arxiv.org/abs/1206.6372
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