Ideal incompressible axisymmetric MHD: Uncovering finite-time singularities
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arXiv
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| Format: | Preprint |
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2025
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| author | Kolluru, Venkata Sai Swetha Pandit, Rahul |
| author_facet | Kolluru, Venkata Sai Swetha Pandit, Rahul |
| contents | We provide compelling numerical evidence for the development of (potential) finite-time singularities in the three-dimensional (3D) axisymmetric, ideal, incompressible magnetohydrodynamic (IMHD) equations, in a wall-bounded cylindrical domain, starting from smooth initial data, for the velocity and magnetic fields. We demonstrate that the nature of the singularity depends crucially on the relative strength C of the velocity and magnetic fields at the time of initialisation: (i) if C < 1, then the swirl components, at the wall, evolve towards square profiles that lead to the intensification of shear at the meridional plane (r = 1, z = L/2) and the development of a finite-time singularity; (ii) if C = 1, there is no temporal evolution; (iii) if C > 1, then the swirl components, at the wall, evolve towards a cusp-type singularity. By examining the spatiotemporal evolution of the pressure, we obtain insights into the development of these singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06842 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ideal incompressible axisymmetric MHD: Uncovering finite-time singularities Kolluru, Venkata Sai Swetha Pandit, Rahul Fluid Dynamics Computational Physics Plasma Physics We provide compelling numerical evidence for the development of (potential) finite-time singularities in the three-dimensional (3D) axisymmetric, ideal, incompressible magnetohydrodynamic (IMHD) equations, in a wall-bounded cylindrical domain, starting from smooth initial data, for the velocity and magnetic fields. We demonstrate that the nature of the singularity depends crucially on the relative strength C of the velocity and magnetic fields at the time of initialisation: (i) if C < 1, then the swirl components, at the wall, evolve towards square profiles that lead to the intensification of shear at the meridional plane (r = 1, z = L/2) and the development of a finite-time singularity; (ii) if C = 1, there is no temporal evolution; (iii) if C > 1, then the swirl components, at the wall, evolve towards a cusp-type singularity. By examining the spatiotemporal evolution of the pressure, we obtain insights into the development of these singularities. |
| title | Ideal incompressible axisymmetric MHD: Uncovering finite-time singularities |
| topic | Fluid Dynamics Computational Physics Plasma Physics |
| url | https://arxiv.org/abs/2507.06842 |