Toroidal vortices in resistive magnetohydrodynamic equilibria

When a time-independent electric current flows toroidally in a uniform ring of electrically conducting fluid, a Lorentz force results, jxB, where j is the local electric current density, and B is the magnetic field it generates. Because of purely geometric effects, the curl of jxB is nonvanishing, and so jxB 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 jxB 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 ringclose 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 cylinderclose quotes limit. copyright 1997 American Institute of Physics