dorsal/arxiv
View SchemaHydrodynamic and magnetohydrodynamic computations inside a rotating sphere
| Authors | P. D. Mininni, D. C. Montgomery, L. Turner |
|---|---|
| Categories | |
| ArXiv ID | physics/0702082 |
| URL | https://arxiv.org/abs/physics/0702082 |
| DOI | 10.1088/1367-2630/9/8/303 |
Abstract
Numerical solutions of the incompressible magnetohydrodynamic (MHD) equations are reported for the interior of a rotating, perfectly-conducting, rigid spherical shell that is insulator-coated on the inside. A previously-reported spectral method is used which relies on a Galerkin expansion in Chandrasekhar-Kendall vector eigenfunctions of the curl. The new ingredient in this set of computations is the rigid rotation of the sphere. After a few purely hydrodynamic examples are sampled (spin down, Ekman pumping, inertial waves), attention is focused on selective decay and the MHD dynamo problem. In dynamo runs, prescribed mechanical forcing excites a persistent velocity field, usually turbulent at modest Reynolds numbers, which in turn amplifies a small seed magnetic field that is introduced. A wide variety of dynamo activity is observed, all at unit magnetic Prandtl number. The code lacks the resolution to probe high Reynolds numbers, but nevertheless interesting dynamo regimes turn out to be plentiful in those parts of parameter space in which the code is accurate. The key control parameters seem to be mechanical and magnetic Reynolds numbers, the Rossby and Ekman numbers (which in our computations are varied mostly by varying the rate of rotation of the sphere) and the amount of mechanical helicity injected. Magnetic energy levels and magnetic dipole behavior are exhibited which fluctuate strongly on a time scale of a few eddy turnover times. These seem to stabilize as the rotation rate is increased until the limit of the code resolution is reached.
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"abstract": "Numerical solutions of the incompressible magnetohydrodynamic (MHD) equations\nare reported for the interior of a rotating, perfectly-conducting, rigid\nspherical shell that is insulator-coated on the inside. A previously-reported\nspectral method is used which relies on a Galerkin expansion in\nChandrasekhar-Kendall vector eigenfunctions of the curl. The new ingredient in\nthis set of computations is the rigid rotation of the sphere. After a few\npurely hydrodynamic examples are sampled (spin down, Ekman pumping, inertial\nwaves), attention is focused on selective decay and the MHD dynamo problem. In\ndynamo runs, prescribed mechanical forcing excites a persistent velocity field,\nusually turbulent at modest Reynolds numbers, which in turn amplifies a small\nseed magnetic field that is introduced. A wide variety of dynamo activity is\nobserved, all at unit magnetic Prandtl number. The code lacks the resolution to\nprobe high Reynolds numbers, but nevertheless interesting dynamo regimes turn\nout to be plentiful in those parts of parameter space in which the code is\naccurate. The key control parameters seem to be mechanical and magnetic\nReynolds numbers, the Rossby and Ekman numbers (which in our computations are\nvaried mostly by varying the rate of rotation of the sphere) and the amount of\nmechanical helicity injected. Magnetic energy levels and magnetic dipole\nbehavior are exhibited which fluctuate strongly on a time scale of a few eddy\nturnover times. These seem to stabilize as the rotation rate is increased until\nthe limit of the code resolution is reached.",
"arxiv_id": "physics/0702082",
"authors": [
"P. D. Mininni",
"D. C. Montgomery",
"L. Turner"
],
"categories": [
"physics.flu-dyn",
"physics.geo-ph",
"physics.plasm-ph"
],
"doi": "10.1088/1367-2630/9/8/303",
"title": "Hydrodynamic and magnetohydrodynamic computations inside a rotating sphere",
"url": "https://arxiv.org/abs/physics/0702082"
},
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