Toroidal vortices in resistive magnetohydrodynamic equilibria
- Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755-3528 (United States)
When a time-independent electric current flows toroidally in a uniform ring of electrically conducting fluid, a Lorentz force results, {bold j{times}B}, where {bold j} is the local electric current density, and {bold B} is the magnetic field it generates. Because of purely geometric effects, the curl of {bold j{times}B} is nonvanishing, and so {bold j{times}B} cannot be balanced by the gradient of any scalar pressure. Taking the curl of the fluid{close_quote}s equation of motion shows that the net effect of the {bold j{times}B} force is to generate toroidal vorticity. Allowed steady states necessarily contain toroidal vortices, with flows in the poloidal directions. The flow pattern is a characteristic {open_quotes}double smoke ring{close_quotes} configuration. The effect seems quite general, although it is analytically simple only in special limits. One limit described here is that of high viscosity (low Reynolds number), with stress-free wall boundary conditions on the velocity field, although it is apparent that similar mechanical motions will result for no-slip boundaries and higher Reynolds numbers. A rather ubiquitous connection between current-carrying toroids and vortex rings seems to be implied, one that disappears in the {open_quotes}straight cylinder{close_quotes} limit. {copyright} {ital 1997 American Institute of Physics.}
- DOE Contract Number:
- FG02-85ER53194
- OSTI ID:
- 475689
- Journal Information:
- Physics of Fluids (1994), Journal Name: Physics of Fluids (1994) Journal Issue: 4 Vol. 9; ISSN 1070-6631; ISSN PHFLE6
- Country of Publication:
- United States
- Language:
- English
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