Magnetic flux ring splitting near a Navier-Stokes singularity

Abstract

OpenAI reports a forced Navier-Stokes flow that becomes singular in finite time, raising the question of its physical consequences. Magnetic reconnection offers a test through the splitting and merging of flux structures. We use resistive magnetohydrodynamics to simulate a magnetic ring driven by an imposed, regularized flow that reproduces the geometry and scaling of the collapsing core. At the nominal singular time, we remove the imposed drive and allow the system to evolve freely. Reconnections before and after release split the ring into two or more daughter rings through bifurcations of the poloidal flux function, with Lorentz feedback selecting the bifurcation type. Unequal winding by the swirl above and below the midplane produces asymmetric toroidal magnetic stresses, unfolding the kinematic pitchfork-like transition into a fold. For single-island splits, the cusp normal form predicts the asymmetry of the daughter rings without adjustable parameters. Three-dimensional simulations retain the splits and merger, confirming that approach to hydrodynamic blow-up can trigger magnetic restructuring.

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BibTeX RIS

BibTeX

@misc{niemi2026magnetic,
  title = {{Magnetic flux ring splitting near a Navier-Stokes singularity}},
  author = {Antti J. Niemi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.22510},
  eprint = {2610.22510},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.22510},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Magnetic flux ring splitting near a Navier-Stokes singularity
AU  - Antti J. Niemi
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.22510
UR  - https://arxiv.org/abs/2610.22510
AB  - OpenAI reports a forced Navier-Stokes flow that becomes singular in finite time, raising the question of its physical consequences. Magnetic reconnection offers a test through the splitting and merging of flux structures. We use resistive magnetohydrodynamics to simulate a magnetic ring driven by an imposed, regularized flow that reproduces the geometry and scaling of the collapsing core. At the nominal singular time, we remove the imposed drive and allow the system to evolve freely. Reconnections before and after release split the ring into two or more daughter rings through bifurcations of the poloidal flux function, with Lorentz feedback selecting the bifurcation type. Unequal winding by the swirl above and below the midplane produces asymmetric toroidal magnetic stresses, unfolding the kinematic pitchfork-like transition into a fold. For single-island splits, the cusp normal form predicts the asymmetry of the daughter rings without adjustable parameters. Three-dimensional simulations retain the splits and merger, confirming that approach to hydrodynamic blow-up can trigger magnetic restructuring.
ER  -

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