  We study desingularization of steady vortex rings in three-dimensional
axisymmetric incompressible Euler fluids with swirl. Using the variational
method, we construct a two-parameter family of steady vortex rings, which
constitute a desingularization of the classical circular vortex filament, in
several kinds of domains. The precise localization of the asymptotic singular
vortex filament is shown to depend on the circulation and the velocity at far
fields of the vortex ring and the geometry of the domains. We also discuss
other qualitative and asymptotic properties of these vortices.
