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New tests for a singularity of ideal MHD

Robert M. Kerr·Axel Brandenburg
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Abstract

Analysis using new calculations with 3 times the resolution of the earlier linked magnetic flux tubes confirms the transition from singular to saturated growth rate reported by Grauer and Marliani \cite{GrauerMar99} for the incompressible cases is confirmed. However, all of the secondary tests point to a transition back to stronger growth rate at a different location at late times. Similar problems in ideal hydrodynamics are discussed, pointing out that initial negative results eventually led to better initial conditions that did show evidence for a singularity of Euler. Whether singular or near-singular growth in ideal MHD is eventually shown, this study could have bearing on fast magnetic reconnection, high energy particle production and coronal heating.

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Robert M. Kerr, Axel Brandenburg. 2000-01-07. New tests for a singularity of ideal MHD. https://arxiv.org/abs/physics/0001016

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