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# Rankine vortex

The Rankine vortex model is an attempt to describe the velocity profile through vortices in real, viscous, fluids. It is named after its creator, William John Macquorn Rankine.

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 mathematical model for the velocity at radius r in the Θ direction in the Rankine vortex is:

$V_\Theta\ (r) = \begin{cases} \frac{V_0r}{R}, & (r \le R) \\ \frac{V_0R}{r}, & (r > R) \end{cases}$
where V0 is the maximum velocity at the peak,
R defines the radius of the vortex core.