  Viscous core correction models are used in free wake simulations to remove
the infinite velocities at the vortex centreline. It will be shown that the
assumption that these corrections converge to the Biot-Savart law in the far
field is not correct for points near the tangent line of a vortex segment.
Furthermore, the self-induced velocity of a vortex ring with a viscous core is
shown to converge to the wrong value. The source of these errors in the model
is identified and an improved model is presented that rectifies the errors. It
results in correct values for the self-induced velocity of a viscous vortex
ring and induced velocities that converge to the values predicted by the
Biot-Savart law for all points in the far field.
