Rankine vortex

The Rankine vortex is a type of 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 forced vortex in its central core, surrounded by a free vortex. In an inviscid fluid, on the other hand, a swirling flow consists entirely of the free vortex with a singularity at its center point instead of the forced vortex core. The tangential velocity^[1] 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 $\mathbf {u} =u_{\theta }\ \mathbf {e_{\theta }}$ .

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

↑ D. J. Acheson (1990). Elementary Fluid Dynamics. Oxford University Press. ISBN 0-19-859679-0.

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Rankine vortex

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Notes