In the case of a vortex, the flow field is purely tangential.

The picture is similar to that of a source but streamlines and equipotential lines are reversed.

The complex potential is


There is again a singularity at the origin, this time associated to the fact that the circulation along any closed curve including the origin is nonzero and equal to tex2html_wrap_inline102 . If the closed curve does not include the origin, the circulation will be zero.