Velocity field within a vortex ring with a large elliptical cross section
This paper derives the velocity field for a steady toroidal vortex with an arbitrary elliptical cross-section by utilizing invariant coordinate sets to exploit metric tensor properties, revealing that vorticity decreases monotonically from the symmetry axis and that the ring's circulation can be either greater or lesser than that of Hill's spherical vortex depending on specific geometric and kinematic parameters.