Deviance information criterion

The Rankine vortex is a model of a vortex in a viscous fluid. A swirling flow in a viscous fluid can be characterized by a forced vortex in its central core, surrounded by a free vortex. On the other hand, in an inviscid fluid the flow consists entirely of the free vortex with an infinite velocity at its center replacing the low velocity core. The tangential velocity of a Rankine vortex with circulation $\mathrm{\Gamma }$ and radius $R$ is

$u_{\theta }(r)=\{\begin{array}{ll}\mathrm{\Gamma }r/(2\pi R^2)& r\le R,\\ \mathrm{\Gamma }/(2\pi r)& r>R.\end{array}$

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

See also

• 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.

Notes

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