Consider a Rankine vortex as shown below. Outside the vortex boundary (indicated by the blue circle), the tangental velocity drops off with distance from the center like 1/r, while inside it increases linearly with radius.

Now, let's superimpose a uniform flow from the left onto the vortex where the flow speed is the same as the maximum tangental speed of the vortex.

Finally, let's look at the streamlines for this combined flow (in red):

Now, let's put this flow into motion and follow the trajectories of three fluid particles.

This material is based upon work supported by the National Science Foundation under Grant No. ATM-0225441.