en>ChrisGualtieri: General Fixes using AWB

2013-10-20T02:32:56Z

General Fixes using AWB

← Older revision		Revision as of 04:32, 20 October 2013
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	~~Andrew Simcox~~ is ~~the name his parents gave him~~ and ~~he completely enjoys this title~~. ~~What me and my family adore is bungee jumping but I've been using on new things recently~~. ~~He is an info officer~~. ~~Ohio is where my house is but my husband wants us to transfer~~.<br><br>~~Here~~ is ~~my weblog~~: ~~are psychics real~~ (~~[http:~~//~~www~~.~~weddingwall~~.~~com~~.~~au/groups/easy~~-~~advice-for-successful-personal~~-development-~~today~~/ ~~look what i found~~])		In [[fluid dynamics]], the '''Lamb–Oseen vortex''' models a line [[vortex]] that decays due to [[viscosity]]. This vortex is named after [[Horace Lamb]] and [[Carl Wilhelm Oseen]].<ref>{{Cite book \| author=Saffman, P. G.; Ablowitz, Mark J.; J. Hinch, E.; Ockendon, J. R.; Olver, Peter J. \| authorlink= \| coauthors= \| title=Vortex dynamics \| year=1992 \| publisher=Cambridge University Press \| location=Cambridge \| isbn=0-521-47739-5 \| pages=}} p. 253.</ref>

			The mathematical model for the [[flow velocity]] in the [[circumference\|circumferential]] <math>\theta</math>–direction in the Lamb–Oseen vortex is:

			:<math>V_\theta(r,t) = \frac{\Gamma}{2\pi r} \left(1-\exp\left(\frac{-r^2}{r_c^2(t)}\right)\right), </math>

			with
			*<math>r</math> = radius,
			*<math>\nu</math> = viscosity,
			*<math>r_c(t)=\sqrt{4\nu t}</math> = core radius of vortex and
			*<math>\Gamma</math> = [[circulation (fluid dynamics)\|circulation]] contained in the vortex.
			The [[radius\|radial]] velocity is equal to zero.

			An alternative definition is to use the peak tangential velocity of the vortex rather than the total circulation

			:<math>V_\theta\left( r \right) =
			V_{\theta \max} \left( 1 + \frac{0.5}{\alpha} \right)
			\frac{r_c}{r}
			\left[ 1 - \exp \left( - \alpha \frac{r^2}{r_c^2} \right)
			\right],
			</math>

			where ''α'' = 1.25643 as used by Devenport et al.<ref>{{cite journal \| author=W.J. Devenport, M.C. Rife, S.I. Liapis and G.J. Follin \| year=1996 \| title= The structure and development of a wing-tip vortex\| journal=Journal of Fluid Mechanics \| volume=312 \| pages=67–106 \| doi=10.1017/S0022112096001929\|bibcode = 1996JFM...312...67D }}</ref>

			==References==
			{{reflist}}

			{{DEFAULTSORT:Lamb-Oseen vortex}}
			[[Category:Vortices]]
			[[Category:Equations of fluid dynamics]]


			{{fluiddynamics-stub}}

en>Rifleman 82: /* See also */ remove tangential

2012-05-15T15:44:16Z

Electron donor - Revision history

en>ChrisGualtieri: General Fixes using AWB

en>Rifleman 82: /* See also */ remove tangential