dorsal/arxiv
View SchemaMagnetohydrodynamic activity inside a sphere
| Authors | P. D. Mininni, D. C. Montgomery |
|---|---|
| Categories | |
| ArXiv ID | physics/0602147 |
| URL | https://arxiv.org/abs/physics/0602147 |
| DOI | 10.1063/1.2393438 |
Abstract
We present a computational method to solve the magnetohydrodynamic equations in spherical geometry. The technique is fully nonlinear and wholly spectral, and uses an expansion basis that is adapted to the geometry: Chandrasekhar-Kendall vector eigenfunctions of the curl. The resulting lower spatial resolution is somewhat offset by being able to build all the boundary conditions into each of the orthogonal expansion functions and by the disappearance of any difficulties caused by singularities at the center of the sphere. The results reported here are for mechanically and magnetically isolated spheres, although different boundary conditions could be studied by adapting the same method. The intent is to be able to study the nonlinear dynamical evolution of those aspects that are peculiar to the spherical geometry at only moderate Reynolds numbers. The code is parallelized, and will preserve to high accuracy the ideal magnetohydrodynamic (MHD) invariants of the system (global energy, magnetic helicity, cross helicity). Examples of results for selective decay and mechanically-driven dynamo simulations are discussed. In the dynamo cases, spontaneous flips of the dipole orientation are observed.
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"abstract": "We present a computational method to solve the magnetohydrodynamic equations\nin spherical geometry. The technique is fully nonlinear and wholly spectral,\nand uses an expansion basis that is adapted to the geometry:\nChandrasekhar-Kendall vector eigenfunctions of the curl. The resulting lower\nspatial resolution is somewhat offset by being able to build all the boundary\nconditions into each of the orthogonal expansion functions and by the\ndisappearance of any difficulties caused by singularities at the center of the\nsphere. The results reported here are for mechanically and magnetically\nisolated spheres, although different boundary conditions could be studied by\nadapting the same method. The intent is to be able to study the nonlinear\ndynamical evolution of those aspects that are peculiar to the spherical\ngeometry at only moderate Reynolds numbers. The code is parallelized, and will\npreserve to high accuracy the ideal magnetohydrodynamic (MHD) invariants of the\nsystem (global energy, magnetic helicity, cross helicity). Examples of results\nfor selective decay and mechanically-driven dynamo simulations are discussed.\nIn the dynamo cases, spontaneous flips of the dipole orientation are observed.",
"arxiv_id": "physics/0602147",
"authors": [
"P. D. Mininni",
"D. C. Montgomery"
],
"categories": [
"physics.flu-dyn",
"physics.geo-ph",
"physics.plasm-ph"
],
"doi": "10.1063/1.2393438",
"title": "Magnetohydrodynamic activity inside a sphere",
"url": "https://arxiv.org/abs/physics/0602147"
},
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