Irrotational Vortices

Question

When trying to find some further information regarding irrotational flows, I encountered the notion of an "irrotational vortex": http://en.wikipedia.org/wiki/Vortex#Irrotational_vortices

In the animation wiki has (see above), one can see that both a rotational vortex, and an irrotational one cause a particle to rotate around itself... I can't understand from their explanation why is the irrotational vortex is "irrotational" ...

Can someone please explain it to me?

Thanks in advance

Answer 1

Here's the animation of the irrotational vertex:

As you can see, the two balls are not themselves rotating, even though they are revolving around the center of the vortex. (You can see the lack of rotation by observing that the white diameters do not change orientation as they move.) This contrasts with a rotational vortex:

Here the balls are themselves rotating, in addition to revolving around the center.

Mathematically, the flow for the first vertex is irrotational in the sense that its curl is equal to zero everywhere except at the very center of the vortex. The curl in the center is not defined, since the flow is not continuous at this point, although a physicist would say that the curl at the center point is infinite.