Rankine vortex

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 (potential or free) vortex.

In reality, very close to the origin, the motion resembles a solid body rotation.

The Rankine vortex model assumes a solid-body rotation inside a cylinder of radius

and a potential vortex outside the cylinder.

of the Rankine vortex, expressed in terms of the cylindrical-coordinate system

is the circulation strength of the Rankine vortex.

Since solid-body rotation is characterized by an azimuthal velocity

is the constant angular velocity, one can also use the parameter

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.