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| The '''Rankine vortex''' is a model of a [[vortex]] in a [[Viscosity|viscous]] fluid. A swirling flow in a viscous fluid can be characterized by a [[Vortex#Forced (rotational) vortex|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<ref>{{cite book | | The title of the writer is Numbers but it's not the most masucline name out there. One of the very best issues in the globe for me is to do aerobics and now I'm attempting to earn cash with it. My day occupation is a meter reader. South Dakota is her birth location but she needs to transfer simply because of her family.<br><br>My web site: [http://www.dynast.co.kr/xe/?document_srl=150618 at home std testing] |
| | title = Elementary Fluid Dynamics
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| | author = D. J. Acheson
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| | publisher = [[Oxford University Press]]
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| | year = 1990
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| | isbn = 0-19-859679-0
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| }}</ref>
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| of a Rankine [[vortex]] with [[Circulation (fluid dynamics)|circulation]] <math>\Gamma</math> and radius <math>R</math> is
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| :<math>u_\theta(r) = \begin{cases} \Gamma r/(2 \pi R^2) & r \le R, \\ \Gamma/(2 \pi r) & r > R. \end{cases}</math> | |
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| The remainder of the velocity components are identically zero, so that the total velocity field is <math>\mathbf{u} = u_\theta\ \mathbf{e_\theta}</math>.
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| == See also ==
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| * [[Vortex]]
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| * [[Viscosity]]
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| * [[Wingtip vortices]]
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| ==External links==
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| *[http://www.atmos.washington.edu/~durrand/animations/vort505/vortanim1.html Streamlines vs. Trajectories in a Translating Rankine Vortex]: an example of a Rankine vortex imposed on a constant velocity field, with animation.
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| ==Notes== | |
| {{reflist}}
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| [[Category:Equations of fluid dynamics]]
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| [[Category:Vortices]]
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| {{fluiddynamics-stub}}
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Revision as of 20:35, 24 February 2014
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