A swirling flow in a viscous fluid can be characterized by a forced vortex in its central core, surrounded by a free vortex. In an inviscid fluid, on the other hand, a swirling flow consists entirely of the free vortex with a singularity at its center point instead of the forced vortex core. The tangential velocity of a Rankine vortex with circulation and radius is
The remainder of the velocity components are identically zero, so that the total velocity field is .
- Streamlines vs. Trajectories in a Translating Rankine Vortex: an example of a Rankine vortex imposed on a constant velocity field, with animation.