Rankine vortex

Velocity distribution in a 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.

A swirling flow in a viscous fluid can be characterized by a central core comprising a forced vortex, surrounded by a free vortex. In an inviscid fluid, on the other hand, a swirling flow consists entirely of a free vortex with a singularity at its center point. The tangential velocity of a Rankine vortex with circulation $\Gamma$ and radius $R$ is

$u_{\theta }(r)={\begin{cases}\Gamma r/(2\pi R^{2})&r\leq R,\\\Gamma /(2\pi r)&r>R.\end{cases}}$

The remainder of the velocity components are identically zero, so that the total velocity field is $\mathbf {u} =u_{\theta }\ \mathbf {e_{\theta }}$.

See also

• Kaufmann (Scully) vortex
• Vortex
• Viscosity
• Wingtip vortices

External links

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