The Rankine vortex model is an attempt to describe the velocity profile through vortices

Vortex

A vortex is a spinning, often turbulent,flow of fluid. Any spiral motion with closed streamlines is vortex flow. The motion of the fluid swirling rapidly around a center is called a vortex...

 in real, viscous

Viscosity

Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

, fluids. It is named after its creator, William John Macquorn Rankine

William John Macquorn Rankine

William John Macquorn Rankine was a Scottish civil engineer, physicist and mathematician. He was a founding contributor, with Rudolf Clausius and William Thomson , to the science of thermodynamics....

.

A swirling flow in a viscous fluid is characterized by a forced vortex in the central core, surrounded by a free vortex. The Rankine vortex best describes this phenomenon. (The velocity profile through an ideal vortex in an inviscid fluid consists entirely of the free vortex with an infinite velocity at its centre. There is no low velocity core.)

The tangential velocity
of a Rankine vortex

Vortex

A vortex is a spinning, often turbulent,flow of fluid. Any spiral motion with closed streamlines is vortex flow. The motion of the fluid swirling rapidly around a center is called a vortex...

 with circulation and radius is


The remainder of the velocity components are identically zero, so that the total velocity field is .

External links

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