1998/12/31 by Robert M. Kerr, Axel Brandenburg · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Classical mechanics #Compressibility #Current sheet #Curvature #Fluid Dynamics and Turbulent Flows #Geometry #Magnetic field #Magnetic flux #Magnetic reconnection #Magnetohydrodynamics #Mathematical analysis #Mechanics #Navier-Stokes equation solutions #Physics #Quantum mechanics #Singularity #Solar and Space Plasma Dynamics #astro-ph #chao-dyn #nlin.CD #physics.plasm-ph
paper · pdf · doi:10.1103/physrevlett.83.1155
4 pages, 4 figures
arxiv created 1999/04/20 · openalex publication_date 1999/08/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Numerical evidence for a finite-time singularity in ideal 3D magnetohydrodynamics is presented. The simulations start from two interlocking magnetic flux rings with no initial velocity. Curvature shrinks the rings until they touch and current sheets form between them. The evidence for a singularity in a finite time tc is that the peak current density behaves like \ensuremath\VertJ\ensuremath\Vert_\ensuremath∞\ensuremath∼1/(tc\ensuremath-t) for a range of sound speeds and initial conditions. For the incompressible calculations \ensuremath\Vert\mathit\ensuremathω\ensuremath\Vert_\ensuremath∞/\ensuremath\VertJ\ensuremath\Vert_\ensuremath∞\ensuremath→const. In resistive reconnection the magnetic helicity is nearly conserved while energy is dissipated.