Lamb–Oseen vortex

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:

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

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

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

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.