Lamb–Oseen vortex

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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.^[1]

The mathematical model for the flow velocity in the circumferential $\theta$ –direction in the Lamb–Oseen vortex is:

$V_{\theta }(r,t)={\frac {\Gamma }{2\pi r}}\left(1-\exp \left({\frac {-r^{2}}{r_{c}^{2}(t)}}\right)\right),$

with

$r$ = radius,
$\nu$ = viscosity,
$r_{c}(t)={\sqrt {4\nu t}}$ = core radius of vortex and
$\Gamma$ = circulation contained in the vortex.

The radial velocity is equal to zero.

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

$V_{\theta }\left(r\right)=V_{{\theta \max }}\left(1+{\frac {0.5}{\alpha }}\right){\frac {r_{c}}{r}}\left[1-\exp \left(-\alpha {\frac {r^{2}}{r_{c}^{2}}}\right)\right],$

where α = 1.25643 as used by Devenport et al.^[2]

References

↑ Saffman, P. G.; Ablowitz, Mark J.; J. Hinch, E.; Ockendon, J. R.; Olver, Peter J. (1992). Vortex dynamics. Cambridge: Cambridge University Press. ISBN 0-521-47739-5. p. 253.
↑ W.J. Devenport, M.C. Rife, S.I. Liapis and G.J. Follin (1996). "The structure and development of a wing-tip vortex". Journal of Fluid Mechanics 312: 67–106. Bibcode:1996JFM...312...67D. doi:10.1017/S0022112096001929.

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