  Based on the solution of Atanasiu et al. (2004), a theoretical model for
axisymmetric vortex flows is derived in the present study by solving the
vorticity transport equation for an inviscid, incompressible fluid in
cylindrical coordinates. The model can describe a variety of axisymmetric flows
with particular boundary conditions at a moderately high Reynolds number. This
paper shows one example: a high Reynolds number laminar vortex ring. The model
can represent a family of vortex rings by specifying the modulus function using
a Rayleigh distribution function. The characteristics of this vortex ring
family are illustrated by numerical methods. For verification, the model
results compare well with the recent direct numerical simulations (DNS) in
terms of the vorticity distribution and streamline patterns, cross-sectional
areas of the vortex core and bubble, and radial vorticity distribution through
the vortex center. Most importantly, the asymmetry and elliptical outline of
the vorticity profile are well captured.
