Lamb–Oseen vortex

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 θ–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,
  • ν = viscosity,
  • r_c(t)=\sqrt{4\nu t} = core radius of vortex and
  • Γ = 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

  1. ^ 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.
  2. ^ 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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