Rankine vortex

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The Rankine vortex is a model of a vortex in a viscous fluid. It is named after its creator, 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 \le 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}.

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