The Rankine vortex is a simple mathematical model of a vortex in a viscous fluid. It is named after its discoverer, William John Macquorn Rankine.

The vortices observed in nature are usually modelled with an irrotational are given by

is the circulation strength is the constant angular velocity can also be used to characterize the vortex.

The vorticity associated with the Rankine vortex is

At all points inside the core of the Rankine vortex, the vorticity is uniform at twice the angular velocity of the core; whereas vorticity is zero at all points outside the core because the flow there is irrotational.

In reality, vortex cores are not always circular; and vorticity is not exactly uniform throughout the vortex core.

See also

• Burgers vortex

• Kaufmann (Scully) vortex – an alternative mathematical simplification for a vortex, with a smoother transition.

• Lamb–Oseen vortex – the exact solution for a free vortex decaying due to viscosity.

References

External links

• Streamlines vs. Trajectories in a Translating Rankine Vortex: an example of a Rankine vortex imposed on a constant velocity field, with animation.