 Rankine oval

A uniform planar stream combined with an equal source and sink produces a closed dividing streamline enclosing them. Outside it the flow approaches the uniform stream; inside it streamlines connect the source and sink. For positive $U,m$ and separation one, the complex velocity is $U-m/[2\pi z(z-1)]$ and the stagnation points are $[1\pm \sqrt{1+2m/(\pi U)}]/2$. Both lie on the dividing streamline, which has zero streamfunction with consistent logarithm branches.