Velocity and vorticity at the eye of a free vortex

[Death eater]

TL;DR

Non-trivial component of velocity vector is tangential?

In free vortex what does it mean " non-trivial component of velocity vector is tangential"? I know only the tangential component of velocity exists in free vortex flow, so what happens at the eye of the vortex ( what happens to vorticity and streamlines to be specific)?

 

[boneh3ad]

The eye of a vortex is a singularity, so the concept of tangential velocity breaks down entirely.