When you pull the plug in a bathtub, you see a good example of a singularity swirl (and a singularity sink).

To detect a singularity swirl, you center a small circle C[r] of radius r at the singularity and calculate a limit of a certain path integral. If this limit is positive, then you have located a counterclockwise singularity swirl. If this limit is negative, then you have located a clockwise singularity swirl.

If this limit is 0, then you have located singularity that has no swirling effect at all.

What limit do you look at?