In the case of a vortex the flow field is purely tangential.
The picture is similar to that of a source but stream lines and isopotential lines are inverted.
The complex potential is
There is again a discontinuity at the origin, this time associated to
the fact that the circulation along any closed curve including the
origin is nonzero and equal to
. If the
closed curve does not include the origin, the circulation is still zero.