dorsal/arxiv
View SchemaA geostrophic-like model for large Hartmann number flows
| Authors | Thierry Alboussiere |
|---|---|
| Categories | |
| ArXiv ID | physics/0503035 |
| URL | https://arxiv.org/abs/physics/0503035 |
| DOI | 10.1017/S0022112004001740 |
| Journal | Journal of Fluid Mechanics 521 (2004) pp. 125-154 |
Abstract
A flow of electrically conducting fluid in the presence of a steady magnetic field has a tendency to become quasi two-dimensional, i.e. uniform in the direction of the magnetic field, except in thin so-called Hartmann boundary layers. The condition for this tendency is that of a strong magnetic field, corresponding to large values of the dimensionless Hartmann number (Ha >> 1). This is analogous to the case of low Ekman number rotating flows, with Ekman layers replacing Hartmann layers. This has been at the origin of the homogeneous model for flows in a rotating frame of reference, with its rich structure: geostrophic contours and shear layers of Stewartson, Munk and Stommel. In magnetohydrodynamics, the characteristic surfaces introduced by Kulikovskii play a role similar to the role of the geostrophic contours. However, a general theory for quasi two-dimensional magnetohydrodynamics is lacking. In this paper, a model is proposed which provides a general framework for quasi two-dimensional magnetohydrodynamic flows. Not only can this model account for otherwise disconnected past results, but it is also used to predict a new type of shear layer, of typical thickness Ha^{-1/4}.
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"abstract": "A flow of electrically conducting fluid in the presence of a steady magnetic\nfield has a tendency to become quasi two-dimensional, i.e. uniform in the\ndirection of the magnetic field, except in thin so-called Hartmann boundary\nlayers. The condition for this tendency is that of a strong magnetic field,\ncorresponding to large values of the dimensionless Hartmann number (Ha \u003e\u003e 1).\nThis is analogous to the case of low Ekman number rotating flows, with Ekman\nlayers replacing Hartmann layers. This has been at the origin of the\nhomogeneous model for flows in a rotating frame of reference, with its rich\nstructure: geostrophic contours and shear layers of Stewartson, Munk and\nStommel. In magnetohydrodynamics, the characteristic surfaces introduced by\nKulikovskii play a role similar to the role of the geostrophic contours.\nHowever, a general theory for quasi two-dimensional magnetohydrodynamics is\nlacking. In this paper, a model is proposed which provides a general framework\nfor quasi two-dimensional magnetohydrodynamic flows. Not only can this model\naccount for otherwise disconnected past results, but it is also used to predict\na new type of shear layer, of typical thickness Ha^{-1/4}.",
"arxiv_id": "physics/0503035",
"authors": [
"Thierry Alboussiere"
],
"categories": [
"physics.flu-dyn"
],
"doi": "10.1017/S0022112004001740",
"journal_ref": "Journal of Fluid Mechanics 521 (2004) pp. 125-154",
"title": "A geostrophic-like model for large Hartmann number flows",
"url": "https://arxiv.org/abs/physics/0503035"
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