dorsal/arxiv
View SchemaKinematic dynamo action in a sphere: Effects of periodic time-dependent flows on solutions with axial dipole symmetry
| Authors | Ashley P. Willis, David Gubbins |
|---|---|
| Categories | |
| ArXiv ID | physics/0409145 |
| URL | https://arxiv.org/abs/physics/0409145 |
| DOI | 10.1080/03091920412331312402 |
Abstract
Choosing a simple class of flows, with characteristics that may be present in the Earth's core, we study the ability to generate a magnetic field when the flow is permitted to oscillate periodically in time. The flow characteristics are parameterised by D, representing a differential rotation, M, a meridional circulation, and C, a component characterising convective rolls. Dynamo action is sensitive to these flow parameters and fails spectacularly for much of the parameter space where magnetic flux is concentrated into small regions. Oscillations of the flow are introduced by varying the flow parameters in time, defining a closed orbit in the space (D,M). Time-dependence appears to smooth out flux concentrations, often enhancing dynamo action. Dynamo action can be impaired, however, when flux concentrations of opposite signs occur close together as smoothing destroys the flux by cancellation. It is possible to produce geomagnetic-type reversals by making the orbit stray into a region where the steady flows generate oscillatory fields. In this case, however, dynamo action was not found to be enhanced by the time-dependence. A novel approach is taken to solving the time-dependent eigenvalue problem, where by combining Floquet theory with a matrix-free Krylov-subspace method we avoid large memory requirements for storing the matrix required by the standard approach.
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"abstract": "Choosing a simple class of flows, with characteristics that may be present in\nthe Earth\u0027s core, we study the ability to generate a magnetic field when the\nflow is permitted to oscillate periodically in time. The flow characteristics\nare parameterised by D, representing a differential rotation, M, a meridional\ncirculation, and C, a component characterising convective rolls. Dynamo action\nis sensitive to these flow parameters and fails spectacularly for much of the\nparameter space where magnetic flux is concentrated into small regions.\n Oscillations of the flow are introduced by varying the flow parameters in\ntime, defining a closed orbit in the space (D,M). Time-dependence appears to\nsmooth out flux concentrations, often enhancing dynamo action. Dynamo action\ncan be impaired, however, when flux concentrations of opposite signs occur\nclose together as smoothing destroys the flux by cancellation.\n It is possible to produce geomagnetic-type reversals by making the orbit\nstray into a region where the steady flows generate oscillatory fields. In this\ncase, however, dynamo action was not found to be enhanced by the\ntime-dependence.\n A novel approach is taken to solving the time-dependent eigenvalue problem,\nwhere by combining Floquet theory with a matrix-free Krylov-subspace method we\navoid large memory requirements for storing the matrix required by the standard\napproach.",
"arxiv_id": "physics/0409145",
"authors": [
"Ashley P. Willis",
"David Gubbins"
],
"categories": [
"physics.geo-ph",
"astro-ph",
"physics.plasm-ph"
],
"doi": "10.1080/03091920412331312402",
"title": "Kinematic dynamo action in a sphere: Effects of periodic time-dependent flows on solutions with axial dipole symmetry",
"url": "https://arxiv.org/abs/physics/0409145"
},
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