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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 | |||
| title = Elementary Fluid Dynamics | |||
| author = D. J. Acheson | |||
| publisher = [[Oxford University Press]] | |||
| year = 1990 | |||
| isbn = 0-19-859679-0 | |||
}}</ref> | |||
of a Rankine [[vortex]] with [[Circulation (fluid dynamics)|circulation]] <math>\Gamma</math> and radius <math>R</math> is | |||
:<math>u_\theta(r) = \begin{cases} \Gamma r/(2 \pi R^2) & r \le R, \\ \Gamma/(2 \pi r) & r > R. \end{cases}</math> | |||
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>. | |||
== See also == | |||
* [[Vortex]] | |||
* [[Viscosity]] | |||
* [[Wingtip vortices]] | |||
==External links== | |||
*[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. | |||
==Notes== | |||
{{reflist}} | |||
[[Category:Equations of fluid dynamics]] | |||
[[Category:Vortices]] | |||
{{fluiddynamics-stub}} | |||
Revision as of 19:04, 16 January 2014
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[1] of a Rankine vortex with circulation and radius is
The remainder of the velocity components are identically zero, so that the total velocity field is .
See also
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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